diff --git a/jedi/inference/compiled/access.py b/jedi/inference/compiled/access.py
index 4177b3c8..3ceab8f1 100644
--- a/jedi/inference/compiled/access.py
+++ b/jedi/inference/compiled/access.py
@@ -211,7 +211,22 @@ class DirectObjectAccess:
     def py__getitem__all_values(self):
         if isinstance(self._obj, dict):
             return [self._create_access_path(v) for v in self._obj.values()]
-        return self.py__iter__list()
+        if isinstance(self._obj, (list, tuple)):
+            return [self._create_access_path(v) for v in self._obj]
+
+        if self.is_instance():
+            cls = DirectObjectAccess(self._inference_state, self._obj.__class__)
+            return cls.py__getitem__all_values()
+
+        try:
+            getitem = self._obj.__getitem__
+        except AttributeError:
+            pass
+        else:
+            annotation = DirectObjectAccess(self._inference_state, getitem).get_return_annotation()
+            if annotation is not None:
+                return [annotation]
+        return None
 
     def py__simple_getitem__(self, index):
         if type(self._obj) not in ALLOWED_GETITEM_TYPES:
@@ -221,8 +236,14 @@ class DirectObjectAccess:
         return self._create_access_path(self._obj[index])
 
     def py__iter__list(self):
-        if not hasattr(self._obj, '__getitem__'):
+        try:
+            iter_method = self._obj.__iter__
+        except AttributeError:
             return None
+        else:
+            p = DirectObjectAccess(self._inference_state, iter_method).get_return_annotation()
+            if p is not None:
+                return [p]
 
         if type(self._obj) not in ALLOWED_GETITEM_TYPES:
             # Get rid of side effects, we won't call custom `__getitem__`s.
diff --git a/jedi/inference/compiled/value.py b/jedi/inference/compiled/value.py
index c4a9eb3f..7b61e717 100644
--- a/jedi/inference/compiled/value.py
+++ b/jedi/inference/compiled/value.py
@@ -166,7 +166,7 @@ class CompiledValue(Value):
             except AttributeError:
                 return super().py__simple_getitem__(index)
         if access is None:
-            return NO_VALUES
+            return super().py__simple_getitem__(index)
 
         return ValueSet([create_from_access_path(self.inference_state, access)])
 
diff --git a/test/test_api/test_interpreter.py b/test/test_api/test_interpreter.py
index b7be471f..4154c072 100644
--- a/test/test_api/test_interpreter.py
+++ b/test/test_api/test_interpreter.py
@@ -603,8 +603,11 @@ def test_dict_getitem(code, types):
 @pytest.mark.parametrize(
     'code, expected', [
         ('DunderCls()[0]', 'int'),
+        ('dunder[0]', 'int'),
         ('next(DunderCls())', 'float'),
+        ('next(dunder)', 'float'),
         ('for x in DunderCls(): x', 'str'),
+        #('for x in dunder: x', 'str'),
     ]
 )
 def test_dunders(class_is_findable, code, expected):
@@ -623,6 +626,8 @@ def test_dunders(class_is_findable, code, expected):
     if not class_is_findable:
         DunderCls.__name__ = 'asdf'
 
+    dunder = DunderCls()
+
     n, = jedi.Interpreter(code, [locals()]).infer()
     assert n.name == expected