diff --git a/src/docstub/_stubs.py b/src/docstub/_stubs.py
index 7947c04..dc50d65 100644
--- a/src/docstub/_stubs.py
+++ b/src/docstub/_stubs.py
@@ -572,8 +572,11 @@ def leave_Param(self, original_node, updated_node):
                         details=details,
                     )
 
-        # Potentially use "Incomplete" except for first param in (class)methods
-        elif not is_self_or_cls and updated_node.annotation is None:
+        has_missing_annotation = (
+            "annotation" not in node_changes and updated_node.annotation is None
+        )
+        # Fallback to "Incomplete" except for first param in (class)methods
+        if has_missing_annotation and not is_self_or_cls:
             node_changes["annotation"] = self._Annotation_Incomplete
             import_ = PyImport.typeshed_Incomplete()
             self._required_imports.add(import_)
diff --git a/tests/test_stubs.py b/tests/test_stubs.py
index 83876c3..6da2098 100644
--- a/tests/test_stubs.py
+++ b/tests/test_stubs.py
@@ -1,3 +1,4 @@
+import logging
 import re
 from textwrap import dedent
 
@@ -278,6 +279,7 @@ def __init__(self, a):
         )
         expected = dedent(
             """
+            from _typeshed import Incomplete
             from typing import ClassVar
             class Foo:
                 a: int
@@ -286,7 +288,7 @@ class Foo:
                 c: list
                 d: ClassVar[bool]
 
-                def __init__(self, a) -> None: ...
+                def __init__(self, a: Incomplete) -> None: ...
             """
         )
         transformer = Py2StubTransformer()
@@ -335,6 +337,7 @@ def test_module_assign_conflict(self, caplog):
 
         assert caplog.messages == ["Keeping existing inline annotation for assignment"]
         assert "ignoring docstring: int" in caplog.records[0].details
+        assert caplog.records[0].levelno == logging.WARNING
 
     def test_module_assign_no_conflict(self, capsys):
         source = dedent(
@@ -405,6 +408,7 @@ class Foo:
         assert expected == result
 
         assert caplog.messages == ["Keeping existing inline annotation for assignment"]
+        assert caplog.records[0].levelno == logging.WARNING
 
     def test_class_assign_no_conflict(self, caplog):
         source = dedent(
@@ -475,6 +479,101 @@ def foo(a: int) -> None: ...
 
         assert caplog.messages == ["Keeping existing inline parameter annotation"]
         assert "ignoring docstring: Sized" in caplog.records[0].details
+        assert caplog.records[0].levelno == logging.WARNING
+
+    def test_missing_param(self, caplog):
+        source = dedent(
+            '''
+            def foo(a, b) -> None:
+                """
+                Parameters
+                ----------
+                a : int
+                """
+            '''
+        )
+        expected = dedent(
+            """
+            from _typeshed import Incomplete
+            def foo(a: int, b: Incomplete) -> None: ...
+            """
+        )
+        transformer = Py2StubTransformer()
+        result = transformer.python_to_stub(source)
+        assert expected == result
+        assert caplog.messages == ["Missing annotation for parameter 'b'"]
+        assert caplog.records[0].levelno == logging.WARNING
+
+    def test_missing_param_inline(self, caplog):
+        source = dedent(
+            """
+            def foo(a: int, b) -> None:
+                pass
+            """
+        )
+        expected = dedent(
+            """
+            from _typeshed import Incomplete
+            def foo(a: int, b: Incomplete) -> None: ...
+            """
+        )
+        transformer = Py2StubTransformer()
+        result = transformer.python_to_stub(source)
+        assert expected == result
+        assert caplog.messages == ["Missing annotation for parameter 'b'"]
+        assert caplog.records[0].levelno == logging.WARNING
+
+    def test_missing_attr(self, caplog):
+        source = dedent(
+            '''
+            class Foo:
+                """
+                Attributes
+                ----------
+                a : ClassVar[int]
+                """
+                a = 3
+                b = True
+            '''
+        )
+        expected = dedent(
+            """
+            from _typeshed import Incomplete
+            from typing import ClassVar
+            class Foo:
+                a: ClassVar[int]
+                b: Incomplete
+            """
+        )
+        transformer = Py2StubTransformer()
+        result = transformer.python_to_stub(source)
+        assert expected == result
+        assert caplog.messages == ["Missing annotation for assignment 'b'"]
+        assert caplog.records[0].levelno == logging.WARNING
+
+    def test_missing_attr_inline(self, caplog):
+        source = dedent(
+            """
+            from typing import ClassVar
+            class Foo:
+                a: ClassVar[int] = 3
+                b = True
+            """
+        )
+        expected = dedent(
+            """
+            from _typeshed import Incomplete
+            from typing import ClassVar
+            class Foo:
+                a: ClassVar[int]
+                b: Incomplete
+            """
+        )
+        transformer = Py2StubTransformer()
+        result = transformer.python_to_stub(source)
+        assert expected == result
+        assert caplog.messages == ["Missing annotation for assignment 'b'"]
+        assert caplog.records[0].levelno == logging.WARNING
 
     def test_return_keep_inline_annotation(self):
         source = dedent(
@@ -515,6 +614,7 @@ def foo() -> int: ...
 
         assert caplog.messages == ["Keeping existing inline return annotation"]
         assert "ignoring docstring: Sized" in caplog.records[0].details
+        assert caplog.records[0].levelno == logging.WARNING
 
     def test_preserved_type_comment(self):
         source = dedent(