diff --git a/jedi/api/completion.py b/jedi/api/completion.py
index 465dd4f7..e28559fd 100644
--- a/jedi/api/completion.py
+++ b/jedi/api/completion.py
@@ -216,6 +216,8 @@ class Completion:
             elif nonterminals[-1] in ('trailer', 'dotted_name') and nodes[-1] == '.':
                 dot = self._module_node.get_leaf_for_position(self._position)
                 completion_names += self._complete_trailer(dot.get_previous_leaf())
+            elif self._is_parameter_completion():
+                pass
             else:
                 completion_names += self._complete_global_scope()
                 completion_names += self._complete_inherited(is_function=False)
@@ -234,6 +236,19 @@ class Completion:
 
         return completion_names
 
+    def _is_parameter_completion(self):
+        tos = self.stack[-1]
+        if tos.nonterminal == 'lambdef' and len(tos.nodes) == 1:
+            # We are at the position `lambda `, where basically the next node
+            # is a param.
+            return True
+        if tos.nonterminal in 'parameters':
+            # Basically we are at the position `foo(`, there's nothing there
+            # yet, so we have no `typedargslist`.
+            return True
+        # var args is for lambdas and typed args for normal functions
+        return tos.nonterminal in ('typedargslist', 'varargslist') and tos.nodes[-1] == ','
+
     def _complete_keywords(self, allowed_transitions):
         for k in allowed_transitions:
             if isinstance(k, str) and k.isalpha():
diff --git a/test/completion/basic.py b/test/completion/basic.py
index 979f4f42..2cd85bcd 100644
--- a/test/completion/basic.py
+++ b/test/completion/basic.py
@@ -319,6 +319,35 @@ def foo3(my_param=my_param):
     pass
 foo3("")
 
+some_default = ''
+#? []
+def foo(my_t
+#? []
+def foo(my_t, my_ty
+#? ['some_default']
+def foo(my_t=some_defa
+#? ['some_default']
+def foo(my_t=some_defa, my_t2=some_defa
+
+#? ['my_type']
+def foo(my_t: lala=some_defa, my_t2: my_typ
+#? ['my_type']
+def foo(my_t: lala=some_defa, my_t2: my_typ
+#? []
+def foo(my_t: lala=some_defa, my_t
+
+#? []
+lambda my_t
+#? []
+lambda my_, my_t
+#? ['some_default']
+lambda x=some_defa
+#? ['some_default']
+lambda y, x=some_defa
+
+# Just make sure we're not in some weird parsing recovery after opening brackets
+def  
+
 # -----------------
 # continuations
 # -----------------
diff --git a/test/completion/parser.py b/test/completion/parser.py
index db88824f..e0159cac 100644
--- a/test/completion/parser.py
+++ b/test/completion/parser.py
@@ -40,4 +40,4 @@ str(def
 class Foo(object):
     @property
     #? ['str']
-    def bar(str
+    def bar(x=str