diff --git a/src/tensor_shape_assert/wrapper.py b/src/tensor_shape_assert/wrapper.py
index 24f9e59..fc667c1 100644
--- a/src/tensor_shape_assert/wrapper.py
+++ b/src/tensor_shape_assert/wrapper.py
@@ -166,8 +166,8 @@ def check_iterable(
             continue
 
         try:
-            constrained_labels = ShapeDescriptor.filter_for_constrained_labels(descriptor.labels)
-            unconstrained_labels = ShapeDescriptor.filter_for_unconstrained_labels(descriptor.labels)
+            constrained_label_annotations = ShapeDescriptor.filter_for_constrained_labels(descriptor.labels)
+            unconstrained_label_annotations = ShapeDescriptor.filter_for_unconstrained_labels(descriptor.labels)
         except KeyError as e:
             raise LabelAnnotationError(
                 f"Label '{e.args[0]}' is not registered. Only registered "
@@ -175,7 +175,7 @@ def check_iterable(
             )
 
         # check labels with constraint fns
-        for label in constrained_labels:
+        for label in constrained_label_annotations:
             constraint_fn = ShapeDescriptor.get_label_constraint_fn(label)
             if constraint_fn is not None:
                 if not constraint_fn(obj):
@@ -184,23 +184,23 @@ def check_iterable(
                         f"label '{label}'."
                     )
 
-        registry_labels = _global_tensor_label_registry.get(obj, frozenset())
+        labels_registered_for_tensor = _global_tensor_label_registry.get(obj, frozenset())
 
-        if must_have_labels:
+        if must_have_labels and labels_registered_for_tensor:
             # check labels annotations for unconstrained labels
-            if unconstrained_labels != registry_labels:
+            if not unconstrained_label_annotations.issubset(labels_registered_for_tensor):
                 raise LabelAnnotationError(
-                    f"Tensor with labels {registry_labels} does not match "
-                    f"annotation with labels {unconstrained_labels}."
+                    f"Tensor with labels {labels_registered_for_tensor} does not match "
+                    f"annotation with labels {unconstrained_label_annotations}."
                 )
-        elif registry_labels and not unconstrained_labels.issubset(registry_labels):
+        elif labels_registered_for_tensor and not unconstrained_label_annotations.issubset(labels_registered_for_tensor):
             raise LabelAnnotationError(
-                f"Tensor with labels {registry_labels} must at least have "
-                f"annotation with labels {unconstrained_labels}."
+                f"Tensor with labels {labels_registered_for_tensor} must at least have "
+                f"annotation with labels {unconstrained_label_annotations}."
             )
-        elif not registry_labels and unconstrained_labels:
+        elif not labels_registered_for_tensor and unconstrained_label_annotations:
             # add to registry if not in registry and annotation has labels
-            label_tensor(obj, unconstrained_labels)
+            label_tensor(obj, unconstrained_label_annotations)
 
         # check shape
         variables = descriptor_to_variables(
diff --git a/src/tensor_shape_assert_test.py b/src/tensor_shape_assert_test.py
index 74f0da6..2d3e794 100644
--- a/src/tensor_shape_assert_test.py
+++ b/src/tensor_shape_assert_test.py
@@ -1778,5 +1778,19 @@ def test_only_overwrite_if_allowed(self):
         with self.assertRaises(LabelAnnotationError):
             label_tensor(x, "test_label_2", overwrite=False)
 
-    # def test_try_to_force_weakref_collision(self):
-    #     ...
\ No newline at end of file
+    def test_no_label_annotation_means_any_label(self):
+        @check_tensor_shapes()
+        def fn(x: ShapedTensor["n m 3"]) -> ShapedTensor["3"]:
+            return xp.sum(x, axis=(0, 1))
+
+        fn(xp.zeros((5, 6, 3)))
+        fn(label_tensor(xp.zeros((5, 6, 3)), "test_label"))
+        fn(label_tensor(xp.zeros((5, 6, 3)), "test_label_2"))
+        fn(label_tensor(xp.zeros((5, 6, 3)), ("test_label", "test_label_2")))
+
+    def test_more_labels_than_annotated_are_allowed(self):
+        @check_tensor_shapes()
+        def fn(x: ShapedTensor["n m 3 test_label"]) -> ShapedTensor["3"]:
+            return xp.sum(x, axis=(0, 1))
+
+        fn(label_tensor(xp.zeros((5, 6, 3)), ("test_label", "test_label_2")))