diff --git a/jedi/inference/compiled/access.py b/jedi/inference/compiled/access.py
index dfca7d9c..b557d450 100644
--- a/jedi/inference/compiled/access.py
+++ b/jedi/inference/compiled/access.py
@@ -5,6 +5,7 @@ import sys
 import operator as op
 from collections import namedtuple
 import warnings
+import re
 
 from jedi._compatibility import unicode, is_py3, builtins, \
     py_version, force_unicode
@@ -491,10 +492,15 @@ class DirectObjectAccess(object):
         if sys.version_info < (3, 5):
             return None, ()
 
-        import typing
-        args = typing.get_args(self._obj)
-        origin = typing.get_origin(self._obj)
-        name = None if origin is None else str(origin)
+        name = None
+        args = ()
+        if safe_getattr(self._obj, '__module__', default='') == 'typing':
+            m = re.match(r'typing.(\w+)\[', repr(self._obj))
+            if m is not None:
+                name = m.group(1)
+
+                import typing
+                args = typing.get_args(self._obj)
         return name, tuple(self._create_access_path(arg) for arg in args)
 
     def needs_type_completions(self):
diff --git a/jedi/inference/compiled/value.py b/jedi/inference/compiled/value.py
index 54814294..a98cd5cf 100644
--- a/jedi/inference/compiled/value.py
+++ b/jedi/inference/compiled/value.py
@@ -273,9 +273,20 @@ class CompiledObject(Value):
             return ValueSet([self])
 
         name, args = self.access_handle.get_annotation_name_and_args()
-        arguments = [create_from_access_path(self.inference_state, path) for path in args]
-        if name == 'typing.Union':
+        arguments = [
+            ValueSet([create_from_access_path(self.inference_state, path)])
+            for path in args
+        ]
+        if name == 'Union':
             return ValueSet.from_sets(arg.execute_annotation() for arg in arguments)
+        elif name:
+            # While with_generics only exists on very specific objects, we
+            # should probably be fine, because we control all the typing
+            # objects.
+            return ValueSet([
+                v.with_generics(arguments)
+                for v in self.inference_state.typing_module.py__getattribute__(name)
+            ]).execute_annotation()
         return super(CompiledObject, self).execute_annotation()
 
     def negate(self):
diff --git a/jedi/inference/gradual/typing.py b/jedi/inference/gradual/typing.py
index 861cc9f0..cfdce3ea 100644
--- a/jedi/inference/gradual/typing.py
+++ b/jedi/inference/gradual/typing.py
@@ -16,7 +16,7 @@ from jedi.inference.names import NameWrapper, ValueName
 from jedi.inference.value.klass import ClassMixin
 from jedi.inference.gradual.base import BaseTypingValue, BaseTypingValueWithGenerics
 from jedi.inference.gradual.type_var import TypeVarClass
-from jedi.inference.gradual.generics import LazyGenericManager
+from jedi.inference.gradual.generics import LazyGenericManager, TupleGenericManager
 
 _PROXY_CLASS_TYPES = 'Tuple Generic Protocol Callable Type'.split()
 _TYPE_ALIAS_TYPES = {
@@ -144,6 +144,14 @@ class ProxyTypingValue(BaseTypingValue):
     index_class = TypingValueWithIndex
     py__simple_getitem__ = None
 
+    def with_generics(self, generics_tuple):
+        return self.index_class.create_cached(
+            self.inference_state,
+            self.parent_context,
+            self._tree_name,
+            generics_manager=TupleGenericManager(generics_tuple)
+        )
+
     def py__getitem__(self, index_value_set, contextualized_node):
         return ValueSet(
             self.index_class.create_cached(
diff --git a/jedi/inference/value/klass.py b/jedi/inference/value/klass.py
index aede4222..7932f995 100644
--- a/jedi/inference/value/klass.py
+++ b/jedi/inference/value/klass.py
@@ -286,6 +286,13 @@ class ClassValue(use_metaclass(CachedMetaClass, ClassMixin, FunctionAndClassBase
             for index_value in index_value_set
         )
 
+    def with_generics(self, generics_tuple):
+        from jedi.inference.gradual.base import GenericClass
+        return GenericClass(
+            self,
+            TupleGenericManager(generics_tuple)
+        )
+
     def define_generics(self, type_var_dict):
         from jedi.inference.gradual.base import GenericClass
 
diff --git a/test/test_api/test_interpreter.py b/test/test_api/test_interpreter.py
index 639a0e64..821ea2d6 100644
--- a/test/test_api/test_interpreter.py
+++ b/test/test_api/test_interpreter.py
@@ -643,29 +643,46 @@ def bar():
 
 @pytest.mark.skipif(sys.version_info < (3, 5), reason="Ignore Python 2, because EOL")
 @pytest.mark.parametrize(
-    'annotations, result', [
-        ({}, []),
-        (None, []),
-        ({'asdf': 'str'}, []),
+    'annotations, result, code', [
+        ({}, [], ''),
+        (None, [], ''),
+        ({'asdf': 'str'}, [], ''),
+
+        ({'return': 'str'}, ['str'], ''),
+        ({'return': 'None'}, ['NoneType'], ''),
+        ({'return': 'str().upper'}, [], ''),
+        ({'return': 'foo()'}, [], ''),
+        ({'return': 'bar()'}, ['float'], ''),
 
-        ({'return': 'str'}, ['str']),
-        ({'return': 'str().upper'}, []),
-        ({'return': 'foo()'}, []),
-        ({'return': 'bar()'}, ['float']),
         # typing is available via globals.
-        ({'return': 'typing.Union[str, int]'}, ['int', 'str']),
-        ({'return': 'typing.Union["str", int]'}, ['int']),
-        ({'return': 'typing.Union["str", 1]'}, []),
-        ({'return': 'typing.Optional[str]'}, ['NoneType', 'str']),
-        ({'return': 'typing.Optional[str, int]'}, []),  # Takes only one arg
+        ({'return': 'typing.Union[str, int]'}, ['int', 'str'], ''),
+        ({'return': 'typing.Union["str", int]'}, ['int'], ''),
+        ({'return': 'typing.Union["str", 1]'}, [], ''),
+        ({'return': 'typing.Optional[str]'}, ['NoneType', 'str'], ''),
+        ({'return': 'typing.Optional[str, int]'}, [], ''),  # Takes only one arg
+        ({'return': 'typing.Any'}, [], ''),
 
-        ({'return': 'decimal.Decimal'}, []),
-        ({'return': 'lalalalallalaa'}, []),
-        ({'return': 'lalalalallalaa.lala'}, []),
+        ({'return': 'typing.Tuple[int, str]'}, ['tuple'], ''),
+        ({'return': 'typing.Tuple[int, str]'}, ['int'], 'x()[0]'),
+        ({'return': 'typing.Tuple[int, str]'}, ['str'], 'x()[1]'),
+        ({'return': 'typing.Tuple[int, str]'}, [], 'x()[2]'),
+
+        ({'return': 'typing.List'}, ['list'], 'list'),
+        ({'return': 'typing.List[int]'}, ['list'], 'list'),
+        ({'return': 'typing.List[int]'}, ['int'], 'x()[0]'),
+        ({'return': 'typing.List[int, str]'}, [], 'x()[0]'),
+
+        ({'return': 'typing.Iterator[int]'}, [], 'x()[0]'),
+        ({'return': 'typing.Iterator[int]'}, ['int'], 'next(x())'),
+        ({'return': 'typing.Iterable[float]'}, ['float'], 'list(x())[0]'),
+
+        ({'return': 'decimal.Decimal'}, [], ''),
+        ({'return': 'lalalalallalaa'}, [], ''),
+        ({'return': 'lalalalallalaa.lala'}, [], ''),
     ]
 )
-def test_string_annotation(annotations, result):
+def test_string_annotation(annotations, result, code):
     x = lambda foo: 1
     x.__annotations__ = annotations
-    defs = jedi.Interpreter('x()', [locals()]).goto_definitions()
+    defs = jedi.Interpreter(code or 'x()', [locals()]).goto_definitions()
     assert [d.name for d in defs] == result