diff --git a/XMLHttpRequest/setrequestheader-bogus-value.htm b/XMLHttpRequest/setrequestheader-bogus-value.htm
index c3aa076c971dc7..15fbb39052526d 100644
--- a/XMLHttpRequest/setrequestheader-bogus-value.htm
+++ b/XMLHttpRequest/setrequestheader-bogus-value.htm
@@ -17,10 +17,9 @@
           assert_throws("SyntaxError", function() { client.setRequestHeader("x-test", value) }, ' given value ' + value+', ');
         });
       }
+      try_value("t\x00t");
       try_value("t\rt");
       try_value("t\nt");
-      try_value("t\bt");
-      try_value("\x7f");
       test(function() {
         var client = new XMLHttpRequest();
         client.open("GET", "...");
diff --git a/fetch/api/headers/header-values-normalize.html b/fetch/api/headers/header-values-normalize.html
new file mode 100644
index 00000000000000..e619c6cddfd72a
--- /dev/null
+++ b/fetch/api/headers/header-values-normalize.html
@@ -0,0 +1,64 @@
+<!doctype html>
+<meta charset=utf8>
+<meta name=timeout content=long>
+<title>Header value normalizing test</title>
+<script src=/resources/testharness.js></script>
+<script src=/resources/testharnessreport.js></script>
+<div id=log></div>
+<script>
+for(let i = 0; i < 0x21; i++) {
+  let fail = false,
+      strip = false
+
+  // REMOVE 0x0B/0x0C exception once https://github.com/w3c/wptserve/issues/111 is fixed
+  if(i === 0x0B || i === 0x0C)
+    continue
+
+  if(i === 0) {
+    fail = true
+  }
+
+  if(i === 0x09 || i === 0x0A || i === 0x0D || i === 0x20) {
+    strip = true
+  }
+
+  let val = String.fromCharCode(i),
+      expectedVal = strip ? "" : val
+  for(let y = 0; y < 3; y++) {
+    let useVal = val,
+        useExpectedVal = expectedVal
+    if(y === 0) {
+      useVal = "x" + val
+      useExpectedVal = "x" + expectedVal
+    } else if(y === 2) {
+      useVal = val + "x"
+      useExpectedVal = expectedVal + "x"
+    }
+
+    async_test((t) => {
+      let xhr = new XMLHttpRequest()
+      xhr.open("POST", "../resources/inspect-headers.py?headers=value-test")
+      if(fail) {
+        assert_throws("SyntaxError", () => xhr.setRequestHeader("value-test", useVal))
+        t.done()
+      } else {
+        xhr.setRequestHeader("value-test", useVal)
+        xhr.onload = t.step_func_done(() => {
+          assert_equals(xhr.getResponseHeader("x-request-value-test"), useExpectedVal)
+        })
+        xhr.send()
+      }
+    }, "XMLHttpRequest with value " + encodeURI(useVal))
+
+    promise_test((t) => {
+      if(fail) {
+        return promise_rejects(t, new TypeError(), fetch("about:blank", { headers: {"value-test": useVal} }))
+      } else {
+        return fetch("../resources/inspect-headers.py?headers=value-test", { headers: {"value-test": useVal} }).then((res) => {
+          assert_equals(res.headers.get("x-request-value-test"), useExpectedVal)
+        })
+      }
+    }, "fetch() with value " + encodeURI(useVal))
+  }
+}
+</script>
diff --git a/fetch/api/headers/header-values.html b/fetch/api/headers/header-values.html
new file mode 100644
index 00000000000000..d45331af7756f5
--- /dev/null
+++ b/fetch/api/headers/header-values.html
@@ -0,0 +1,41 @@
+<!doctype html>
+<meta charset=utf8>
+<meta name=timeout content=long>
+<title>Header value test</title>
+<script src=/resources/testharness.js></script>
+<script src=/resources/testharnessreport.js></script>
+<div id=log></div>
+<script>
+for(let i = 0; i < 0x100; i++) {
+  let fail = false
+  if(i === 0 || i === 0x0A || i === 0x0D) {
+    fail = true
+  }
+
+  let val = "x" + String.fromCharCode(i) + "x"
+  async_test((t) => {
+    let xhr = new XMLHttpRequest()
+    xhr.open("POST", "../resources/inspect-headers.py?headers=value-test")
+    if(fail) {
+      assert_throws("SyntaxError", () => xhr.setRequestHeader("value-test", val))
+      t.done()
+    } else {
+      xhr.setRequestHeader("value-test", val)
+      xhr.onload = t.step_func_done(() => {
+        assert_equals(xhr.getResponseHeader("x-request-value-test"), val)
+      })
+      xhr.send()
+    }
+  }, "XMLHttpRequest with value " + encodeURI(val))
+
+  promise_test((t) => {
+    if(fail) {
+      return promise_rejects(t, new TypeError(), fetch("about:blank", { headers: {"value-test": val} }))
+    } else {
+      return fetch("../resources/inspect-headers.py?headers=value-test", { headers: {"value-test": val} }).then((res) => {
+        assert_equals(res.headers.get("x-request-value-test"), val)
+      })
+    }
+  }, "fetch() with value " + encodeURI(val))
+}
+</script>
