diff --git a/jedi/api/classes.py b/jedi/api/classes.py
index d1566700..662c09e7 100644
--- a/jedi/api/classes.py
+++ b/jedi/api/classes.py
@@ -687,7 +687,7 @@ class ParamDefinition(Definition):
         :param execute_annotation: If False, the values are not executed and
             you get classes instead of instances.
         """
-        return _values_to_definitions(self._name.infer_annotation(**kwargs))
+        return _values_to_definitions(self._name.infer_annotation(ignore_stars=True, **kwargs))
 
     def to_string(self):
         return self._name.to_string()
diff --git a/jedi/inference/gradual/annotation.py b/jedi/inference/gradual/annotation.py
index f291a1e4..76d76078 100644
--- a/jedi/inference/gradual/annotation.py
+++ b/jedi/inference/gradual/annotation.py
@@ -107,8 +107,10 @@ def _split_comment_param_declaration(decl_text):
 
 
 @inference_state_method_cache()
-def infer_param(execution_context, param):
+def infer_param(execution_context, param, ignore_stars=False):
     values = _infer_param(execution_context, param)
+    if ignore_stars:
+        return values
     inference_state = execution_context.inference_state
     if param.star_count == 1:
         tuple_ = builtin_from_name(inference_state, 'tuple')
diff --git a/jedi/inference/names.py b/jedi/inference/names.py
index ff06bf2e..0a6a668c 100644
--- a/jedi/inference/names.py
+++ b/jedi/inference/names.py
@@ -242,11 +242,11 @@ class ParamName(BaseTreeParamName):
     def annotation_node(self):
         return self._get_param_node().annotation
 
-    def infer_annotation(self, execute_annotation=True):
-        node = self.annotation_node
-        if node is None:
-            return NO_VALUES
-        values = self.parent_context.parent_context.infer_node(node)
+    def infer_annotation(self, execute_annotation=True, ignore_stars=False):
+        from jedi.inference.gradual.annotation import infer_param
+        values = infer_param(
+            self.parent_context, self._get_param_node(),
+            ignore_stars=ignore_stars)
         if execute_annotation:
             values = values.execute_annotation()
         return values
@@ -299,6 +299,9 @@ class ParamName(BaseTreeParamName):
         return Parameter.POSITIONAL_OR_KEYWORD
 
     def infer(self):
+        values = self.infer_annotation()
+        if values:
+            return values
         return self.get_param().infer()
 
     def get_param(self):
diff --git a/jedi/inference/param.py b/jedi/inference/param.py
index f3d721e0..1b66c05c 100644
--- a/jedi/inference/param.py
+++ b/jedi/inference/param.py
@@ -33,9 +33,8 @@ class ExecutedParam(object):
     def infer(self, use_hints=True):
         if use_hints:
             doc_params = docstrings.infer_param(self._execution_context, self._param_node)
-            ann = self.infer_annotations().execute_annotation()
-            if ann or doc_params:
-                return ann | doc_params
+            if doc_params:
+                return doc_params
 
         return self._lazy_value.infer()
 
diff --git a/test/completion/pep0484_basic.py b/test/completion/pep0484_basic.py
index aef5437c..ba7cab18 100644
--- a/test/completion/pep0484_basic.py
+++ b/test/completion/pep0484_basic.py
@@ -24,7 +24,7 @@ def function_parameters(a: A, b, c: str, d: int, e: str, f: str, g: int=4):
     d
     #? str()
     e
-    #? int() str()
+    #? str()
     f
     # int()
     g