diff --git a/leval/evaluator.py b/leval/evaluator.py
index 55ee2c3..2afcea6 100644
--- a/leval/evaluator.py
+++ b/leval/evaluator.py
@@ -22,7 +22,12 @@
 
 DEFAULT_ALLOWED_CONTAINER_TYPES = frozenset((tuple, set))
 DEFAULT_ALLOWED_CONSTANT_TYPES = frozenset(
-    (str, int, float, NoneType),
+    (
+        str,
+        int,  # NB: this implicitly includes bool
+        float,
+        NoneType,
+    ),
 )
 
 
diff --git a/leval/excs.py b/leval/excs.py
index 2e13b38..9a0773b 100644
--- a/leval/excs.py
+++ b/leval/excs.py
@@ -29,6 +29,10 @@ class InvalidOperands(InvalidOperation):
     pass
 
 
+class InvalidAttribute(InvalidOperation):
+    pass
+
+
 class NoSuchValue(NameError, EvaluatorError):
     pass
 
diff --git a/leval/utils.py b/leval/utils.py
index 8e94da4..94452a0 100644
--- a/leval/utils.py
+++ b/leval/utils.py
@@ -1,7 +1,7 @@
 import ast
 from typing import Tuple
 
-from leval.excs import InvalidOperation
+from leval.excs import InvalidAttribute
 
 
 def expand_name(node: ast.Attribute) -> Tuple[str, ...]:
@@ -18,8 +18,13 @@ def walk_attr(kid):
             walk_attr(kid.value)
         elif isinstance(kid, ast.Name):
             attr_bits.append(kid.id)
+        elif isinstance(kid, ast.Constant):
+            raise InvalidAttribute(
+                f"Accessing attributes of constants ({kid}) is not allowed",
+                node=node,
+            )
         else:
-            raise InvalidOperation(  # pragma: no cover
+            raise InvalidAttribute(  # pragma: no cover
                 f"Unsupported attribute structure in {node}",
                 node=node,
             )
diff --git a/leval_tests/test_leval.py b/leval_tests/test_leval.py
index 60f5ced..f95e8f0 100644
--- a/leval_tests/test_leval.py
+++ b/leval_tests/test_leval.py
@@ -5,6 +5,7 @@
 
 from leval.evaluator import Evaluator
 from leval.excs import (
+    InvalidAttribute,
     InvalidOperands,
     InvalidOperation,
     NoSuchFunction,
@@ -81,7 +82,10 @@
     ),
     ("Can't access weird methods off valid names", "abs.__class__", NoSuchValue),
     ("Arbitrary Python code is not allowed", "if x > a:\n    hello()", SyntaxError),
-    ("Can't access attributes off constants", "(3).__class__", InvalidOperation),
+    ("Can't access numeric constants' attributes", "(3).__class__", InvalidAttribute),
+    ("Can't access Nones' attributes", "None.__class__", InvalidAttribute),
+    ("Can't access Falses' attributes", "False.__class__", InvalidAttribute),
+    ("Can't access Trues' attributes", "True.__class__", InvalidAttribute),
     (
         "Walruses aren't allowed",
         "(a := 3) + 8",