diff --git a/lib/test.js b/lib/test.js
index bf3cbd8a..6fb86242 100644
--- a/lib/test.js
+++ b/lib/test.js
@@ -417,12 +417,12 @@ Test.prototype.error
 = Test.prototype.iferror
 = error;
 
-function equal(a, b, msg, extra) {
+function strictEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
-    this._assert(a == b, {
-        message: defined(msg, 'should be equal'),
+    this._assert(is(a, b), {
+        message: defined(msg, 'should be strictly equal'),
         operator: 'equal',
         actual: a,
         expected: b,
@@ -432,103 +432,92 @@ function equal(a, b, msg, extra) {
 Test.prototype.equal
 = Test.prototype.equals
 = Test.prototype.isEqual
-= equal;
-
-function strictEqual(a, b, msg, extra) {
-    if (arguments.length < 2) {
-        throw new TypeError('two arguments must be provided to compare');
-    }
-    this._assert(is(a, b), {
-        message: defined(msg, 'should be strictly equal'),
-        operator: 'strictEqual',
-        actual: a,
-        expected: b,
-        extra: extra
-    });
-}
-Test.prototype.strictEqual
+= Test.prototype.strictEqual
 = Test.prototype.strictEquals
 = Test.prototype.is
 = strictEqual;
 
-function notEqual(a, b, msg, extra) {
+function notStrictEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
-    this._assert(a != b, {
-        message: defined(msg, 'should not be equal'),
+    this._assert(!is(a, b), {
+        message: defined(msg, 'should not be strictly equal'),
         operator: 'notEqual',
         actual: a,
         expected: b,
         extra: extra
     });
 }
+
 Test.prototype.notEqual
 = Test.prototype.notEquals
 = Test.prototype.isNotEqual
 = Test.prototype.doesNotEqual
 = Test.prototype.isInequal
-= notEqual;
+= Test.prototype.notStrictEqual
+= Test.prototype.notStrictEquals
+= Test.prototype.isNot
+= Test.prototype.not
+= notStrictEqual;
 
-function notStrictEqual(a, b, msg, extra) {
+function looseEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
-    this._assert(!is(a, b), {
-        message: defined(msg, 'should not be strictly equal'),
-        operator: 'notStrictEqual',
+    this._assert(a == b, {
+        message: defined(msg, 'should be loosely equal'),
+        operator: 'looseEqual',
         actual: a,
         expected: b,
         extra: extra
     });
 }
-Test.prototype.notStrictEqual
-= Test.prototype.notStrictEquals
-= Test.prototype.isNot
-= Test.prototype.not
-= notStrictEqual;
 
-function tapeDeepEqual(a, b, msg, extra) {
+Test.prototype.looseEqual
+= Test.prototype.looseEquals
+= looseEqual;
+
+function notLooseEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
-    this._assert(deepEqual(a, b, { strict: true }), {
-        message: defined(msg, 'should be equivalent'),
-        operator: 'deepEqual',
+    this._assert(a != b, {
+        message: defined(msg, 'should not be loosely equal'),
+        operator: 'notLooseEqual',
         actual: a,
         expected: b,
         extra: extra
     });
 }
-Test.prototype.deepEqual
-= Test.prototype.deepEquals
-= Test.prototype.isEquivalent
-= Test.prototype.same
-= tapeDeepEqual;
+Test.prototype.notLooseEqual
+= Test.prototype.notLooseEquals
+= notLooseEqual;
 
-function deepLooseEqual(a, b, msg, extra) {
+function tapeDeepEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
-    this._assert(deepEqual(a, b), {
-        message: defined(msg, 'should be equivalent'),
-        operator: 'deepLooseEqual',
+    this._assert(deepEqual(a, b, { strict: true }), {
+        message: defined(msg, 'should be deeply equivalent'),
+        operator: 'deepEqual',
         actual: a,
         expected: b,
         extra: extra
     });
 }
-Test.prototype.deepLooseEqual
-= Test.prototype.looseEqual
-= Test.prototype.looseEquals
-= deepLooseEqual;
+Test.prototype.deepEqual
+= Test.prototype.deepEquals
+= Test.prototype.isEquivalent
+= Test.prototype.same
+= tapeDeepEqual;
 
 function notDeepEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
     this._assert(!deepEqual(a, b, { strict: true }), {
-        message: defined(msg, 'should not be equivalent'),
+        message: defined(msg, 'should not be deeply equivalent'),
         operator: 'notDeepEqual',
         actual: a,
         expected: b,
@@ -546,12 +535,28 @@ Test.prototype.notDeepEqual
 = Test.prototype.isInequivalent
 = notDeepEqual;
 
+function deepLooseEqual(a, b, msg, extra) {
+    if (arguments.length < 2) {
+        throw new TypeError('two arguments must be provided to compare');
+    }
+    this._assert(deepEqual(a, b), {
+        message: defined(msg, 'should be loosely deeply equivalent'),
+        operator: 'deepLooseEqual',
+        actual: a,
+        expected: b,
+        extra: extra
+    });
+}
+
+Test.prototype.deepLooseEqual
+= deepLooseEqual;
+
 function notDeepLooseEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
     this._assert(!deepEqual(a, b), {
-        message: defined(msg, 'should be equivalent'),
+        message: defined(msg, 'should not be loosely deeply equivalent'),
         operator: 'notDeepLooseEqual',
         actual: a,
         expected: b,
@@ -559,8 +564,6 @@ function notDeepLooseEqual(a, b, msg, extra) {
     });
 }
 Test.prototype.notDeepLooseEqual
-= Test.prototype.notLooseEqual
-= Test.prototype.notLooseEquals
 = notDeepLooseEqual;
 
 Test.prototype['throws'] = function (fn, expected, msg, extra) {
diff --git a/readme.markdown b/readme.markdown
index 756eeba1..3e66ca7d 100644
--- a/readme.markdown
+++ b/readme.markdown
@@ -27,8 +27,8 @@ test('timing test', function (t) {
 $ node example/timing.js
 TAP version 13
 # timing test
-ok 1 should be equal
-not ok 2 should be equal
+ok 1 should be strictly equal
+not ok 2 should be strictly equal
   ---
     operator: equal
     expected: 100
@@ -217,27 +217,27 @@ Aliases: `t.ifError()`, `t.ifErr()`, `t.iferror()`
 
 ## t.equal(actual, expected, msg)
 
-Assert that `actual == expected` with an optional description of the assertion `msg`.
+Assert that `Object.is(actual, expected)` with an optional description of the assertion `msg`.
 
-Aliases: `t.equals()`, `t.isEqual()`
+Aliases: `t.equals()`, `t.isEqual()`, `t.strictEqual()`, `t.strictEquals()`, `t.is()`
 
-## t.strictEqual(actual, expected, msg)
+## t.notEqual(actual, expected, msg)
 
-Assert that `Object.is(actual, expected)` with an optional description of the assertion `msg`.
+Assert that `!Object.is(actual, expected)` with an optional description of the assertion `msg`.
 
-Aliases: `t.is()`, `t.strictEqual()`, `t.strictEquals()`
+Aliases: `t.notEquals()`, `t.isNotEqual()`, `t.doesNotEqual()`, `t.isInequal()`, `t.notStrictEqual()`, `t.notStrictEquals()`, `t.isNot()`, `t.not()`
 
-## t.notEqual(actual, expected, msg)
+## t.looseEqual(actual, expected, msg)
 
-Assert that `actual != expected` with an optional description of the assertion `msg`.
+Assert that `actual == expected` with an optional description of the assertion `msg`.
 
-Aliases: `t.notEquals()`, `t.isNotEqual()`, `t.doesNotEqual()`, `t.isInequal()`
+Aliases: `t.looseEquals()`
 
-## t.notStrictEqual(actual, expected, msg)
+## t.notLooseEqual(actual, expected, msg)
 
-Assert that `!Object.is(actual, expected)` with an optional description of the assertion `msg`.
+Assert that `actual != expected` with an optional description of the assertion `msg`.
 
-Aliases: `t.notStrictEqual()`, `t.notStrictEquals()`, `t.isNot()`, `t.not()`
+Aliases: `t.notLooseEquals()`
 
 ## t.deepEqual(actual, expected, msg)
 
@@ -263,8 +263,6 @@ Assert that `actual` and `expected` have the same structure and nested values us
 [node's deepEqual() algorithm](https://github.com/substack/node-deep-equal)
 with loose comparisons (`==`) on leaf nodes and an optional description of the assertion `msg`.
 
-Aliases: `t.looseEqual()`, `t.looseEquals()`
-
 ## t.notDeepLooseEqual(actual, expected, msg)
 
 Assert that `actual` and `expected` do not have the same structure and nested values using
@@ -347,14 +345,14 @@ Pass in test files to run as arguments:
 $ node tap.js test/x.js test/y.js
 TAP version 13
 # (anonymous)
-not ok 1 should be equal
+not ok 1 should be strictly equal
   ---
     operator: equal
     expected: "boop"
     actual:   "beep"
   ...
 # (anonymous)
-ok 2 should be equal
+ok 2 should be strictly equal
 ok 3 (unnamed assert)
 # wheee
 ok 4 (unnamed assert)
@@ -387,10 +385,10 @@ The output for this runner is:
 ```sh
 $ node object.js test/x.js test/y.js
 {"type":"test","name":"(anonymous)","id":0}
-{"id":0,"ok":false,"name":"should be equal","operator":"equal","actual":"beep","expected":"boop","error":{},"test":0,"type":"assert"}
+{"id":0,"ok":false,"name":"should be strictly equal","operator":"equal","actual":"beep","expected":"boop","error":{},"test":0,"type":"assert"}
 {"type":"end","test":0}
 {"type":"test","name":"(anonymous)","id":1}
-{"id":0,"ok":true,"name":"should be equal","operator":"equal","actual":2,"expected":2,"test":1,"type":"assert"}
+{"id":0,"ok":true,"name":"should be strictly equal","operator":"equal","actual":2,"expected":2,"test":1,"type":"assert"}
 {"id":1,"ok":true,"name":"(unnamed assert)","operator":"ok","actual":true,"expected":true,"test":1,"type":"assert"}
 {"type":"end","test":1}
 {"type":"test","name":"wheee","id":2}
diff --git a/test/array.js b/test/array.js
index 0184fb26..d150b18e 100644
--- a/test/array.js
+++ b/test/array.js
@@ -14,11 +14,11 @@ tap.test('array test', function (tt) {
         tt.same(rows.toString('utf8'), [
             'TAP version 13',
             '# array',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
-            'ok 5 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
+            'ok 5 should be deeply equivalent',
             '',
             '1..5',
             '# tests 5',
diff --git a/test/circular-things.js b/test/circular-things.js
index c2745cad..ae9462f0 100644
--- a/test/circular-things.js
+++ b/test/circular-things.js
@@ -15,7 +15,7 @@ tap.test('circular test', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# circular\n'
-            + 'not ok 1 should be equal\n'
+            + 'not ok 1 should be strictly equal\n'
             + '  ---\n'
             + '    operator: equal\n'
             + '    expected: |-\n'
@@ -24,7 +24,7 @@ tap.test('circular test', function (assert) {
             + '      { circular: [Circular] }\n'
             + '    at: Test.<anonymous> ($TEST/circular-things.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should be equal\n'
+            + '      Error: should be strictly equal\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/circular-things.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
diff --git a/test/deep-equal-failure.js b/test/deep-equal-failure.js
index fa32d651..a3f16b92 100644
--- a/test/deep-equal-failure.js
+++ b/test/deep-equal-failure.js
@@ -21,7 +21,7 @@ tap.test('deep equal failure', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# deep equal\n'
-            + 'not ok 1 should be equal\n'
+            + 'not ok 1 should be strictly equal\n'
             + '  ---\n'
             + '    operator: equal\n'
             + '    expected: |-\n'
@@ -30,7 +30,7 @@ tap.test('deep equal failure', function (assert) {
             + '      { a: 1 }\n'
             + '    at: Test.<anonymous> ($TEST/deep-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should be equal\n'
+            + '      Error: should be strictly equal\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/deep-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -55,7 +55,7 @@ tap.test('deep equal failure', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should be equal',
+            name: 'should be strictly equal',
             diag: {
                 operator: 'equal',
                 expected: '{ b: 2 }',
@@ -82,7 +82,7 @@ tap.test('deep equal failure, depth 6, with option', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# deep equal\n'
-            + 'not ok 1 should be equal\n'
+            + 'not ok 1 should be strictly equal\n'
             + '  ---\n'
             + '    operator: equal\n'
             + '    expected: |-\n'
@@ -91,7 +91,7 @@ tap.test('deep equal failure, depth 6, with option', function (assert) {
             + '      { a: { a1: { a2: { a3: { a4: { a5: 1 } } } } } }\n'
             + '    at: Test.<anonymous> ($TEST/deep-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should be equal\n'
+            + '      Error: should be strictly equal\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/deep-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -116,7 +116,7 @@ tap.test('deep equal failure, depth 6, with option', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should be equal',
+            name: 'should be strictly equal',
             diag: {
                 operator: 'equal',
                 expected: '{ a: { a1: { a2: { a3: { a4: { a5: 2 } } } } } }',
@@ -143,7 +143,7 @@ tap.test('deep equal failure, depth 6, without option', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# deep equal\n'
-            + 'not ok 1 should be equal\n'
+            + 'not ok 1 should be strictly equal\n'
             + '  ---\n'
             + '    operator: equal\n'
             + '    expected: |-\n'
@@ -152,7 +152,7 @@ tap.test('deep equal failure, depth 6, without option', function (assert) {
             + '      { a: { a1: { a2: { a3: { a4: [Object] } } } } }\n'
             + '    at: Test.<anonymous> ($TEST/deep-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should be equal\n'
+            + '      Error: should be strictly equal\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/deep-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -177,7 +177,7 @@ tap.test('deep equal failure, depth 6, without option', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should be equal',
+            name: 'should be strictly equal',
             diag: {
                 operator: 'equal',
                 expected: '{ a: { a1: { a2: { a3: { a4: [Object] } } } } }',
diff --git a/test/default-messages.js b/test/default-messages.js
index 307ec89b..359c98a5 100644
--- a/test/default-messages.js
+++ b/test/default-messages.js
@@ -5,6 +5,8 @@ var path = require('path');
 var spawn = require('child_process').spawn;
 var concat = require('concat-stream');
 
+var stripFullStack = require('./common').stripFullStack;
+
 tap.test('default messages', function (t) {
     t.plan(1);
 
@@ -12,22 +14,37 @@ tap.test('default messages', function (t) {
 
     ps.stdout.pipe(concat(function (rows) {
 
-        t.same(rows.toString('utf8'), [
+        t.same(stripFullStack(rows.toString('utf8')), [
             'TAP version 13',
             '# default messages',
             'ok 1 should be truthy',
             'ok 2 should be falsy',
-            'ok 3 should be equal',
-            'ok 4 should not be equal',
-            'ok 5 should be equivalent',
-            'ok 6 should be equivalent',
-            'ok 7 should be equivalent',
-            '',
-            '1..7',
-            '# tests 7',
-            '# pass  7',
+            'ok 3 should be strictly equal',
+            'ok 4 should not be strictly equal',
+            'ok 5 should be loosely equal',
+            'ok 6 should not be loosely equal',
+            'ok 7 should be strictly equal',
+            'ok 8 should not be strictly equal',
+            'ok 9 should be deeply equivalent',
+            'not ok 10 should not be deeply equivalent',
+            '  ---',
+            '    operator: notDeepEqual',
+            '    expected: true',
+            '    actual:   true',
+            '    at: Test.<anonymous> ($TEST/messages/defaults.js:$LINE:$COL)',
+            '    stack: |-',
+            '      Error: should not be deeply equivalent',
+            '          [... stack stripped ...]',
+            '          at Test.<anonymous> ($TEST/messages/defaults.js:$LINE:$COL)',
+            '          [... stack stripped ...]',
+            '  ...',
+            'ok 11 should be loosely deeply equivalent',
+            'ok 12 should not be loosely deeply equivalent',
             '',
-            '# ok'
+            '1..12',
+            '# tests 12',
+            '# pass  11',
+            '# fail  1'
         ].join('\n') + '\n\n');
     }));
 });
diff --git a/test/double_end.js b/test/double_end.js
index f7cd9e35..5dc6e2a0 100644
--- a/test/double_end.js
+++ b/test/double_end.js
@@ -41,7 +41,7 @@ test(function (t) {
         t.equal(stripped, [
             'TAP version 13',
             '# double end',
-            'ok 1 should be equal',
+            'ok 1 should be strictly equal',
             'not ok 2 .end() already called',
             '  ---',
             '    operator: fail',
diff --git a/test/edge-cases.js b/test/edge-cases.js
index 00b0072c..93b6fceb 100644
--- a/test/edge-cases.js
+++ b/test/edge-cases.js
@@ -15,39 +15,69 @@ tap.test('edge cases', function (tt) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# zeroes\n'
-            + 'ok 1 0 equal to -0\n'
-            + 'ok 2 -0 equal to 0\n'
-            + 'not ok 3 0 notEqual to -0\n'
+            + 'not ok 1 0 equal to -0\n'
             + '  ---\n'
-            + '    operator: notEqual\n'
+            + '    operator: equal\n'
             + '    expected: |-\n'
             + '      -0\n'
             + '    actual: |-\n'
             + '      0\n'
             + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: 0 notEqual to -0\n'
+            + '      Error: 0 equal to -0\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 4 -0 notEqual to 0\n'
+            + 'not ok 2 -0 equal to 0\n'
             + '  ---\n'
-            + '    operator: notEqual\n'
+            + '    operator: equal\n'
+            + '    expected: |-\n'
+            + '      0\n'
+            + '    actual: |-\n'
+            + '      -0\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: -0 equal to 0\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'ok 3 0 notEqual to -0\n'
+            + 'ok 4 -0 notEqual to 0\n'
+            + 'ok 5 0 looseEqual to -0\n'
+            + 'ok 6 -0 looseEqual to 0\n'
+            + 'not ok 7 0 notLooseEqual to -0\n'
+            + '  ---\n'
+            + '    operator: notLooseEqual\n'
+            + '    expected: |-\n'
+            + '      -0\n'
+            + '    actual: |-\n'
+            + '      0\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: 0 notLooseEqual to -0\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 8 -0 notLooseEqual to 0\n'
+            + '  ---\n'
+            + '    operator: notLooseEqual\n'
             + '    expected: |-\n'
             + '      0\n'
             + '    actual: |-\n'
             + '      -0\n'
             + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: -0 notEqual to 0\n'
+            + '      Error: -0 notLooseEqual to 0\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 5 0 strictEqual to -0\n'
+            + 'not ok 9 0 strictEqual to -0\n'
             + '  ---\n'
-            + '    operator: strictEqual\n'
+            + '    operator: equal\n'
             + '    expected: |-\n'
             + '      -0\n'
             + '    actual: |-\n'
@@ -59,9 +89,9 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 6 -0 strictEqual to 0\n'
+            + 'not ok 10 -0 strictEqual to 0\n'
             + '  ---\n'
-            + '    operator: strictEqual\n'
+            + '    operator: equal\n'
             + '    expected: |-\n'
             + '      0\n'
             + '    actual: |-\n'
@@ -73,11 +103,11 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 7 0 notStrictEqual to -0\n'
-            + 'ok 8 -0 notStrictEqual to 0\n'
-            + 'ok 9 0 deepLooseEqual to -0\n'
-            + 'ok 10 -0 deepLooseEqual to 0\n'
-            + 'not ok 11 0 notDeepLooseEqual to -0\n'
+            + 'ok 11 0 notStrictEqual to -0\n'
+            + 'ok 12 -0 notStrictEqual to 0\n'
+            + 'ok 13 0 deepLooseEqual to -0\n'
+            + 'ok 14 -0 deepLooseEqual to 0\n'
+            + 'not ok 15 0 notDeepLooseEqual to -0\n'
             + '  ---\n'
             + '    operator: notDeepLooseEqual\n'
             + '    expected: |-\n'
@@ -91,7 +121,7 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 12 -0 notDeepLooseEqual to 0\n'
+            + 'not ok 16 -0 notDeepLooseEqual to 0\n'
             + '  ---\n'
             + '    operator: notDeepLooseEqual\n'
             + '    expected: |-\n'
@@ -105,7 +135,7 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 13 0 deepEqual to -0\n'
+            + 'not ok 17 0 deepEqual to -0\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: |-\n'
@@ -119,7 +149,7 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 14 -0 deepEqual to 0\n'
+            + 'not ok 18 -0 deepEqual to 0\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: |-\n'
@@ -133,26 +163,39 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 15 0 notDeepEqual to -0\n'
-            + 'ok 16 -0 notDeepEqual to 0\n'
+            + 'ok 19 0 notDeepEqual to -0\n'
+            + 'ok 20 -0 notDeepEqual to 0\n'
             + '# NaNs\n'
-            + 'not ok 17 NaN equal to NaN\n'
+            + 'ok 21 NaN equal to NaN\n'
+            + 'not ok 22 NaN notEqual to NaN\n'
             + '  ---\n'
-            + '    operator: equal\n'
+            + '    operator: notEqual\n'
             + '    expected: NaN\n'
             + '    actual:   NaN\n'
             + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: NaN equal to NaN\n'
+            + '      Error: NaN notEqual to NaN\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 18 NaN notEqual to NaN\n'
-            + 'ok 19 NaN strictEqual to NaN\n'
-            + 'not ok 20 NaN notStrictEqual to NaN\n'
+            + 'not ok 23 NaN looseEqual to NaN\n'
             + '  ---\n'
-            + '    operator: notStrictEqual\n'
+            + '    operator: looseEqual\n'
+            + '    expected: NaN\n'
+            + '    actual:   NaN\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: NaN looseEqual to NaN\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'ok 24 NaN notLooseEqual to NaN\n'
+            + 'ok 25 NaN strictEqual to NaN\n'
+            + 'not ok 26 NaN notStrictEqual to NaN\n'
+            + '  ---\n'
+            + '    operator: notEqual\n'
             + '    expected: NaN\n'
             + '    actual:   NaN\n'
             + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
@@ -162,7 +205,7 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 21 NaN deepLooseEqual to NaN\n'
+            + 'not ok 27 NaN deepLooseEqual to NaN\n'
             + '  ---\n'
             + '    operator: deepLooseEqual\n'
             + '    expected: NaN\n'
@@ -174,9 +217,9 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 22 NaN notDeepLooseEqual to NaN\n'
-            + 'ok 23 NaN deepEqual to NaN\n'
-            + 'not ok 24 NaN notDeepEqual to NaN\n'
+            + 'ok 28 NaN notDeepLooseEqual to NaN\n'
+            + 'ok 29 NaN deepEqual to NaN\n'
+            + 'not ok 30 NaN notDeepEqual to NaN\n'
             + '  ---\n'
             + '    operator: notDeepEqual\n'
             + '    expected: NaN\n'
@@ -188,10 +231,10 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + '\n1..24\n'
-            + '# tests 24\n'
-            + '# pass  12\n'
-            + '# fail  12\n'
+            + '\n1..30\n'
+            + '# tests 30\n'
+            + '# pass  15\n'
+            + '# fail  15\n'
         );
     }));
 
@@ -201,6 +244,11 @@ tap.test('edge cases', function (tt) {
         t.notEqual(0, -0, '0 notEqual to -0');
         t.notEqual(-0, 0, '-0 notEqual to 0');
 
+        t.looseEqual(0, -0, '0 looseEqual to -0');
+        t.looseEqual(-0, 0, '-0 looseEqual to 0');
+        t.notLooseEqual(0, -0, '0 notLooseEqual to -0');
+        t.notLooseEqual(-0, 0, '-0 notLooseEqual to 0');
+
         t.strictEqual(0, -0, '0 strictEqual to -0');
         t.strictEqual(-0, 0, '-0 strictEqual to 0');
         t.notStrictEqual(0, -0, '0 notStrictEqual to -0');
@@ -223,6 +271,9 @@ tap.test('edge cases', function (tt) {
         t.equal(NaN, NaN, 'NaN equal to NaN');
         t.notEqual(NaN, NaN, 'NaN notEqual to NaN');
 
+        t.looseEqual(NaN, NaN, 'NaN looseEqual to NaN');
+        t.notLooseEqual(NaN, NaN, 'NaN notLooseEqual to NaN');
+
         t.strictEqual(NaN, NaN, 'NaN strictEqual to NaN');
         t.notStrictEqual(NaN, NaN, 'NaN notStrictEqual to NaN');
 
diff --git a/test/end-as-callback.js b/test/end-as-callback.js
index 1781dcbe..84a751d7 100644
--- a/test/end-as-callback.js
+++ b/test/end-as-callback.js
@@ -13,10 +13,10 @@ tap.test("tape assert.end as callback", function (tt) {
             'TAP version 13',
             '# do a task and write',
             'ok 1 null',
-            'ok 2 should be equal',
+            'ok 2 should be strictly equal',
             '# do a task and write fail',
             'ok 3 null',
-            'ok 4 should be equal',
+            'ok 4 should be strictly equal',
             'not ok 5 Error: fail',
             getStackTrace(rows), // tap error stack
             '',
diff --git a/test/exit.js b/test/exit.js
index 093c46c1..326520f3 100644
--- a/test/exit.js
+++ b/test/exit.js
@@ -15,11 +15,11 @@ tap.test('exit ok', function (t) {
             'TAP version 13',
             '# array',
             '# hi',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
-            'ok 5 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
+            'ok 5 should be deeply equivalent',
             '',
             '1..5',
             '# tests 5',
@@ -45,18 +45,18 @@ tap.test('exit fail', function (t) {
         t.same(stripFullStack(rows.toString('utf8')), [
             'TAP version 13',
             '# array',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
-            'not ok 5 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
+            'not ok 5 should be deeply equivalent',
             '  ---',
             '    operator: deepEqual',
             '    expected: [ [ 1, 2, [ 3, 4444 ] ], [ 5, 6 ] ]',
             '    actual:   [ [ 1, 2, [ 3, 4 ] ], [ 5, 6 ] ]',
             '    at: Test.<anonymous> ($TEST/exit/fail.js:$LINE:$COL)',
             '    stack: |-',
-            '      Error: should be equivalent',
+            '      Error: should be deeply equivalent',
             '          [... stack stripped ...]',
             '          at $TEST/exit/fail.js:$LINE:$COL',
             '          at eval (eval at <anonymous> ($TEST/exit/fail.js:$LINE:$COL))',
@@ -86,11 +86,11 @@ tap.test('too few exit', function (t) {
         t.same(stripFullStack(rows.toString('utf8')), [
             'TAP version 13',
             '# array',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
-            'ok 5 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
+            'ok 5 should be deeply equivalent',
             'not ok 6 plan != count',
             '  ---',
             '    operator: fail',
diff --git a/test/fail.js b/test/fail.js
index 5b68fc87..6221b4c6 100644
--- a/test/fail.js
+++ b/test/fail.js
@@ -15,18 +15,18 @@ tap.test('array test', function (tt) {
         tt.same(stripFullStack(rows.toString('utf8')), [
             'TAP version 13',
             '# array',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
-            'not ok 5 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
+            'not ok 5 should be deeply equivalent',
             '  ---',
             '    operator: deepEqual',
             '    expected: [ [ 1, 2, [ 3, 4444 ] ], [ 5, 6 ] ]',
             '    actual:   [ [ 1, 2, [ 3, 4 ] ], [ 5, 6 ] ]',
             '    at: Test.<anonymous> ($TEST/fail.js:$LINE:$COL)',
             '    stack: |-',
-            '      Error: should be equivalent',
+            '      Error: should be deeply equivalent',
             '          [... stack stripped ...]',
             '          at $TEST/fail.js:$LINE:$COL',
             '          at eval (eval at <anonymous> ($TEST/fail.js:$LINE:$COL))',
diff --git a/test/messages/defaults.js b/test/messages/defaults.js
index ee3bfc1e..e9672147 100644
--- a/test/messages/defaults.js
+++ b/test/messages/defaults.js
@@ -3,12 +3,23 @@
 var test = require('../../');
 
 test('default messages', function (t) {
-    t.plan(7);
+    t.plan(12);
+
     t.ok(true);
     t.notOk(false);
+
     t.equal(true, true);
     t.notEqual(true, false);
+
+    t.looseEqual(true, true);
+    t.notLooseEqual(true, false);
+
+    t.strictEqual(true, true);
+    t.notStrictEqual(true, false);
+
     t.deepEqual(true, true);
+    t.notDeepEqual(true, true);
+
     t.deepLooseEqual(true, true);
     t.notDeepLooseEqual(true, false);
 });
diff --git a/test/nested.js b/test/nested.js
index 7eefe90b..98c9398c 100644
--- a/test/nested.js
+++ b/test/nested.js
@@ -13,11 +13,11 @@ tap.test('array test', function (tt) {
         tt.same(rows.toString('utf8'), [
             'TAP version 13',
             '# nested array test',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
-            'ok 5 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
+            'ok 5 should be deeply equivalent',
             '# inside test',
             'ok 6 should be truthy',
             'ok 7 should be truthy',
diff --git a/test/not-deep-equal-failure.js b/test/not-deep-equal-failure.js
index 08b0df5f..849135ab 100644
--- a/test/not-deep-equal-failure.js
+++ b/test/not-deep-equal-failure.js
@@ -21,7 +21,7 @@ tap.test('deep equal failure', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# not deep equal\n'
-            + 'not ok 1 should not be equivalent\n'
+            + 'not ok 1 should not be deeply equivalent\n'
             + '  ---\n'
             + '    operator: notDeepEqual\n'
             + '    expected: |-\n'
@@ -30,7 +30,7 @@ tap.test('deep equal failure', function (assert) {
             + '      { b: 2 }\n'
             + '    at: Test.<anonymous> ($TEST/not-deep-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should not be equivalent\n'
+            + '      Error: should not be deeply equivalent\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/not-deep-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -55,7 +55,7 @@ tap.test('deep equal failure', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should not be equivalent',
+            name: 'should not be deeply equivalent',
             diag: {
                 operator: 'notDeepEqual',
                 expected: '{ b: 2 }',
@@ -82,7 +82,7 @@ tap.test('not deep equal failure, depth 6, with option', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# not deep equal\n'
-            + 'not ok 1 should not be equivalent\n'
+            + 'not ok 1 should not be deeply equivalent\n'
             + '  ---\n'
             + '    operator: notDeepEqual\n'
             + '    expected: |-\n'
@@ -91,7 +91,7 @@ tap.test('not deep equal failure, depth 6, with option', function (assert) {
             + '      { a: { a1: { a2: { a3: { a4: { a5: 1 } } } } } }\n'
             + '    at: Test.<anonymous> ($TEST/not-deep-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should not be equivalent\n'
+            + '      Error: should not be deeply equivalent\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/not-deep-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -116,7 +116,7 @@ tap.test('not deep equal failure, depth 6, with option', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should not be equivalent',
+            name: 'should not be deeply equivalent',
             diag: {
                 operator: 'notDeepEqual',
                 expected: '{ a: { a1: { a2: { a3: { a4: { a5: 1 } } } } } }',
@@ -143,7 +143,7 @@ tap.test('not deep equal failure, depth 6, without option', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# not deep equal\n'
-            + 'not ok 1 should not be equivalent\n'
+            + 'not ok 1 should not be deeply equivalent\n'
             + '  ---\n'
             + '    operator: notDeepEqual\n'
             + '    expected: |-\n'
@@ -152,7 +152,7 @@ tap.test('not deep equal failure, depth 6, without option', function (assert) {
             + '      { a: { a1: { a2: { a3: { a4: [Object] } } } } }\n'
             + '    at: Test.<anonymous> ($TEST/not-deep-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should not be equivalent\n'
+            + '      Error: should not be deeply equivalent\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/not-deep-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -177,7 +177,7 @@ tap.test('not deep equal failure, depth 6, without option', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should not be equivalent',
+            name: 'should not be deeply equivalent',
             diag: {
                 operator: 'notDeepEqual',
                 expected: '{ a: { a1: { a2: { a3: { a4: [Object] } } } } }',
diff --git a/test/not-equal-failure.js b/test/not-equal-failure.js
index f3c528aa..a02abd7d 100644
--- a/test/not-equal-failure.js
+++ b/test/not-equal-failure.js
@@ -21,14 +21,14 @@ tap.test('not equal failure', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# not equal\n'
-            + 'not ok 1 should not be equal\n'
+            + 'not ok 1 should not be strictly equal\n'
             + '  ---\n'
             + '    operator: notEqual\n'
             + '    expected: 2\n'
             + '    actual:   2\n'
             + '    at: Test.<anonymous> ($TEST/not-equal-failure.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should not be equal\n'
+            + '      Error: should not be strictly equal\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/not-equal-failure.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
@@ -53,7 +53,7 @@ tap.test('not equal failure', function (assert) {
         assert.deepEqual(data, {
             ok: false,
             id: 1,
-            name: 'should not be equal',
+            name: 'should not be strictly equal',
             diag: {
                 operator: 'notEqual',
                 expected: '2',
diff --git a/test/numerics.js b/test/numerics.js
index 7c3f7554..a7a40204 100644
--- a/test/numerics.js
+++ b/test/numerics.js
@@ -15,35 +15,61 @@ tap.test('numerics', function (tt) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# numeric strings\n'
-            + 'ok 1 number equal to string\n'
-            + 'ok 2 string equal to number\n'
-            + 'not ok 3 number notEqual to string\n'
+            + 'not ok 1 number equal to string\n'
             + '  ---\n'
-            + '    operator: notEqual\n'
+            + '    operator: equal\n'
             + '    expected: \'3\'\n'
             + '    actual:   3\n'
             + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: number notEqual to string\n'
+            + '      Error: number equal to string\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 4 string notEqual to number\n'
+            + 'not ok 2 string equal to number\n'
             + '  ---\n'
-            + '    operator: notEqual\n'
+            + '    operator: equal\n'
             + '    expected: 3\n'
             + '    actual:   \'3\'\n'
             + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: string notEqual to number\n'
+            + '      Error: string equal to number\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 5 number strictEqual to string\n'
+            + 'ok 3 number notEqual to string\n'
+            + 'ok 4 string notEqual to number\n'
+            + 'ok 5 number looseEqual to string\n'
+            + 'ok 6 string looseEqual to number\n'
+            + 'not ok 7 number notLooseEqual to string\n'
             + '  ---\n'
-            + '    operator: strictEqual\n'
+            + '    operator: notLooseEqual\n'
+            + '    expected: \'3\'\n'
+            + '    actual:   3\n'
+            + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: number notLooseEqual to string\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 8 string notLooseEqual to number\n'
+            + '  ---\n'
+            + '    operator: notLooseEqual\n'
+            + '    expected: 3\n'
+            + '    actual:   \'3\'\n'
+            + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: string notLooseEqual to number\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 9 number strictEqual to string\n'
+            + '  ---\n'
+            + '    operator: equal\n'
             + '    expected: \'3\'\n'
             + '    actual:   3\n'
             + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
@@ -53,9 +79,9 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 6 string strictEqual to number\n'
+            + 'not ok 10 string strictEqual to number\n'
             + '  ---\n'
-            + '    operator: strictEqual\n'
+            + '    operator: equal\n'
             + '    expected: 3\n'
             + '    actual:   \'3\'\n'
             + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
@@ -65,11 +91,11 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 7 number notStrictEqual to string\n'
-            + 'ok 8 string notStrictEqual to number\n'
-            + 'ok 9 number deepLooseEqual to string\n'
-            + 'ok 10 string deepLooseEqual to number\n'
-            + 'not ok 11 number notDeepLooseEqual to string\n'
+            + 'ok 11 number notStrictEqual to string\n'
+            + 'ok 12 string notStrictEqual to number\n'
+            + 'ok 13 number deepLooseEqual to string\n'
+            + 'ok 14 string deepLooseEqual to number\n'
+            + 'not ok 15 number notDeepLooseEqual to string\n'
             + '  ---\n'
             + '    operator: notDeepLooseEqual\n'
             + '    expected: \'3\'\n'
@@ -81,7 +107,7 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 12 string notDeepLooseEqual to number\n'
+            + 'not ok 16 string notDeepLooseEqual to number\n'
             + '  ---\n'
             + '    operator: notDeepLooseEqual\n'
             + '    expected: 3\n'
@@ -93,7 +119,7 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 13 number deepEqual to string\n'
+            + 'not ok 17 number deepEqual to string\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: \'3\'\n'
@@ -105,7 +131,7 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 14 string deepEqual to number\n'
+            + 'not ok 18 string deepEqual to number\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: 3\n'
@@ -117,12 +143,12 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 15 number notDeepEqual to string\n'
-            + 'ok 16 string notDeepEqual to number\n'
-            + '\n1..16\n'
-            + '# tests 16\n'
-            + '# pass  8\n'
-            + '# fail  8\n'
+            + 'ok 19 number notDeepEqual to string\n'
+            + 'ok 20 string notDeepEqual to number\n'
+            + '\n1..20\n'
+            + '# tests 20\n'
+            + '# pass  10\n'
+            + '# fail  10\n'
         );
     }));
 
@@ -132,6 +158,11 @@ tap.test('numerics', function (tt) {
         t.notEqual(3, '3', 'number notEqual to string');
         t.notEqual('3', 3, 'string notEqual to number');
 
+        t.looseEqual(3, '3', 'number looseEqual to string');
+        t.looseEqual('3', 3, 'string looseEqual to number');
+        t.notLooseEqual(3, '3', 'number notLooseEqual to string');
+        t.notLooseEqual('3', 3, 'string notLooseEqual to number');
+
         t.strictEqual(3, '3', 'number strictEqual to string');
         t.strictEqual('3', 3, 'string strictEqual to number');
         t.notStrictEqual(3, '3', 'number notStrictEqual to string');
diff --git a/test/todo_single.js b/test/todo_single.js
index 01591e27..eeb7d265 100644
--- a/test/todo_single.js
+++ b/test/todo_single.js
@@ -16,7 +16,7 @@ tap.test('tape todo test', function (assert) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# TODO failure\n'
-            + 'not ok 1 should be equal # TODO\n'
+            + 'not ok 1 should be strictly equal # TODO\n'
             + '  ---\n'
             + '    operator: equal\n'
             + '    expected: false\n'
diff --git a/test/too_many.js b/test/too_many.js
index f9cc7c4f..dc47b7b2 100644
--- a/test/too_many.js
+++ b/test/too_many.js
@@ -15,10 +15,10 @@ tap.test('array test', function (tt) {
         tt.same(stripFullStack(rows.toString('utf8')), [
             'TAP version 13',
             '# array',
-            'ok 1 should be equivalent',
-            'ok 2 should be equivalent',
-            'ok 3 should be equivalent',
-            'ok 4 should be equivalent',
+            'ok 1 should be deeply equivalent',
+            'ok 2 should be deeply equivalent',
+            'ok 3 should be deeply equivalent',
+            'ok 4 should be deeply equivalent',
             'not ok 5 plan != count',
             '  ---',
             '    operator: fail',
@@ -34,7 +34,7 @@ tap.test('array test', function (tt) {
             '          at Test.<anonymous> ($TEST/too_many.js:$LINE:$COL)',
             '          [... stack stripped ...]',
             '  ...',
-            'ok 6 should be equivalent',
+            'ok 6 should be deeply equivalent',
             '',
             '1..6',
             '# tests 6',
diff --git a/test/undef.js b/test/undef.js
index 2e210545..3f935be0 100644
--- a/test/undef.js
+++ b/test/undef.js
@@ -15,7 +15,7 @@ tap.test('array test', function (tt) {
             stripFullStack(body.toString('utf8')),
             'TAP version 13\n'
             + '# undef\n'
-            + 'not ok 1 should be equivalent\n'
+            + 'not ok 1 should be deeply equivalent\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: |-\n'
@@ -24,7 +24,7 @@ tap.test('array test', function (tt) {
             + '      {}\n'
             + '    at: Test.<anonymous> ($TEST/undef.js:$LINE:$COL)\n'
             + '    stack: |-\n'
-            + '      Error: should be equivalent\n'
+            + '      Error: should be deeply equivalent\n'
             + '          [... stack stripped ...]\n'
             + '          at Test.<anonymous> ($TEST/undef.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'