diff --git a/src/packaging/utils.py b/src/packaging/utils.py
index 23450953..608f9b95 100644
--- a/src/packaging/utils.py
+++ b/src/packaging/utils.py
@@ -110,7 +110,9 @@ def parse_wheel_filename(
     name_part = parts[0]
     # See PEP 427 for the rules on escaping the project name.
     if "__" in name_part or re.match(r"^[\w\d._]*$", name_part, re.UNICODE) is None:
-        raise InvalidWheelFilename(f"Invalid project name: {filename!r}")
+        raise InvalidWheelFilename(
+            f"Invalid wheel filename (invalid project name {name_part!r}): {filename!r}"
+        )
     name = canonicalize_name(name_part)
 
     try:
@@ -120,12 +122,18 @@ def parse_wheel_filename(
             f"Invalid wheel filename (invalid version): {filename!r}"
         ) from e
 
+    if str(version) != parts[1]:
+        raise InvalidWheelFilename(
+            f"Invalid wheel filename (non-normalized version): {filename!r}"
+        )
+
     if dashes == 5:
         build_part = parts[2]
         build_match = _build_tag_regex.match(build_part)
         if build_match is None:
             raise InvalidWheelFilename(
-                f"Invalid build number: {build_part} in {filename!r}"
+                f"Invalid wheel filename (invalid build number {build_part!r}): "
+                f"{filename!r}"
             )
         build = cast(BuildTag, (int(build_match.group(1)), build_match.group(2)))
     else:
diff --git a/tests/test_utils.py b/tests/test_utils.py
index a8cc8d71..d6ae2cc2 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -144,22 +144,41 @@ def test_parse_wheel_filename(filename, name, version, build, tags):
 
 
 @pytest.mark.parametrize(
-    ("filename"),
+    ("filename", "expected"),
     [
-        ("foo-1.0.whl"),  # Missing tags
-        ("foo-1.0-py3-none-any.wheel"),  # Incorrect file extension (`.wheel`)
-        ("foo__bar-1.0-py3-none-any.whl"),  # Invalid name (`__`)
-        ("foo#bar-1.0-py3-none-any.whl"),  # Invalid name (`#`)
-        ("foobar-1.x-py3-none-any.whl"),  # Invalid version (`1.x`)
-        # Build number doesn't start with a digit (`abc`)
-        ("foo-1.0-abc-py3-none-any.whl"),
-        ("foo-1.0-200-py3-none-any-junk.whl"),  # Too many dashes (`-junk`)
+        ("foo-1.0.whl", "wrong number of parts"),
+        ("foo-1.0-py3-none-any.wheel", "extension must be '.whl'"),
+        ("foo__bar-1.0-py3-none-any.whl", "invalid project name"),
+        ("foo#bar-1.0-py3-none-any.whl", "invalid project name"),
+        ("foobar-1.x-py3-none-any.whl", "invalid version"),
+        ("foo-1.0-abc-py3-none-any.whl", "invalid build number"),
+        ("foo-1.0-200-py3-none-any-junk.whl", "wrong number of parts"),
+        ("foo-01.0.0-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.1RC1-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.1.a1-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.1_a1-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.0a.1-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.1alpha1-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.1beta2-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.1c2-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2a-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2_post2-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2post2-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2.post.2-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.0.r4-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2.post-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2dev2-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.2.dev-py3-none-any.whl", "non-normalized version"),
+        ("foo-1.0+ubuntu_1-py3-none-any.whl", "non-normalized version"),
+        ("foo-v1.0-py3-none-any.whl", "non-normalized version"),
     ],
 )
-def test_parse_wheel_invalid_filename(filename):
-    with pytest.raises(InvalidWheelFilename):
+def test_parse_wheel_invalid_filename(filename, expected):
+    with pytest.raises(InvalidWheelFilename) as e:
         parse_wheel_filename(filename)
 
+    assert expected in str(e.value)
+
 
 @pytest.mark.parametrize(
     ("filename", "name", "version"),