diff --git a/jsonschema/tests/test_cli.py b/jsonschema/tests/test_cli.py
index eafc05d6c..f9c8c621e 100644
--- a/jsonschema/tests/test_cli.py
+++ b/jsonschema/tests/test_cli.py
@@ -10,9 +10,9 @@
 import sys
 import tempfile
 
-try:
+try:  # pragma: no cover
     from importlib import metadata
-except ImportError:
+except ImportError:  # pragma: no cover
     import importlib_metadata as metadata
 
 from pyrsistent import m
@@ -36,7 +36,7 @@ def __init__(self, *args, **kwargs):
         def iter_errors(self, instance):
             if errors:
                 return errors.pop()
-            return []
+            return []  # pragma: no cover
 
         @classmethod
         def check_schema(self, schema):
diff --git a/jsonschema/tests/test_jsonschema_test_suite.py b/jsonschema/tests/test_jsonschema_test_suite.py
index 23a34c9af..6a367ddd5 100644
--- a/jsonschema/tests/test_jsonschema_test_suite.py
+++ b/jsonschema/tests/test_jsonschema_test_suite.py
@@ -42,7 +42,7 @@ def skipper(test):
 
 
 def missing_format(checker):
-    def missing_format(test):
+    def missing_format(test):  # pragma: no cover
         schema = test.schema
         if (
             schema is True
@@ -93,7 +93,7 @@ def narrow_unicode_build(test):  # pragma: no cover
         return
 
 
-if sys.version_info < (3, 9):
+if sys.version_info < (3, 9):  # pragma: no cover
     message = "Rejecting leading zeros is 3.9+"
     allowed_leading_zeros = skip(
         message=message,
@@ -103,7 +103,7 @@ def narrow_unicode_build(test):  # pragma: no cover
         ),
     )
 else:
-    def allowed_leading_zeros(test):
+    def allowed_leading_zeros(test):  # pragma: no cover
         return
 
 
diff --git a/jsonschema/tests/test_types.py b/jsonschema/tests/test_types.py
index 21e8312cc..8a4537c7e 100644
--- a/jsonschema/tests/test_types.py
+++ b/jsonschema/tests/test_types.py
@@ -28,18 +28,6 @@ def is_object_or_named_tuple(checker, instance):
     return is_namedtuple(instance)
 
 
-def coerce_named_tuple(fn):
-    def coerced(validator, value, instance, schema):
-        if is_namedtuple(instance):
-            instance = instance._asdict()
-        return fn(validator, value, instance, schema)
-    return coerced
-
-
-required = coerce_named_tuple(_validators.required)
-properties = coerce_named_tuple(_validators.properties)
-
-
 class TestTypeChecker(TestCase):
     def test_is_type(self):
         checker = TypeChecker({"two": equals_2})
@@ -139,6 +127,9 @@ def int_or_str_int(checker, instance):
         with self.assertRaises(ValidationError):
             validator.validate(4.4)
 
+        with self.assertRaises(ValidationError):
+            validator.validate("foo")
+
     def test_object_can_be_extended(self):
         schema = {"type": "object"}
 
@@ -179,6 +170,16 @@ def test_object_extensions_can_handle_custom_validators(self):
             "object", is_object_or_named_tuple,
         )
 
+        def coerce_named_tuple(fn):
+            def coerced(validator, value, instance, schema):
+                if is_namedtuple(instance):
+                    instance = instance._asdict()
+                return fn(validator, value, instance, schema)
+            return coerced
+
+        required = coerce_named_tuple(_validators.required)
+        properties = coerce_named_tuple(_validators.properties)
+
         CustomValidator = extend(
             Draft4Validator,
             type_checker=type_checker,
@@ -194,6 +195,12 @@ def test_object_extensions_can_handle_custom_validators(self):
         with self.assertRaises(ValidationError):
             validator.validate(Point(x="not an integer", y=5))
 
+        # As well as still handle objects.
+        validator.validate({"x": 4, "y": 5})
+
+        with self.assertRaises(ValidationError):
+            validator.validate({"x": "not an integer", "y": 5})
+
     def test_unknown_type(self):
         with self.assertRaises(UnknownType) as e:
             Draft4Validator({}).is_type(12, "some unknown type")