diff --git a/jedi/inference/gradual/typing.py b/jedi/inference/gradual/typing.py
index add28177..e0ebcb96 100644
--- a/jedi/inference/gradual/typing.py
+++ b/jedi/inference/gradual/typing.py
@@ -145,6 +145,24 @@ class TypingClassWithIndex(BaseTypingClassWithGenerics):
             generics_manager
         )
 
+    def infer_type_vars(self, value_set):
+        annotation_generics = self.get_generics()
+
+        if not annotation_generics:
+            return {}
+
+        annotation_name = self.py__name__()
+        if annotation_name == 'Optional':
+            # Optional[T] is equivalent to Union[T, None]. In Jedi unions
+            # are represented by members within a ValueSet, so we extract
+            # the T from the Optional[T] by removing the None value.
+            none = builtin_from_name(self.inference_state, u'None')
+            return annotation_generics[0].infer_type_vars(
+                value_set.filter(lambda x: x != none),
+            )
+
+        return {}
+
 
 class ProxyTypingValue(BaseTypingValue):
     index_class = TypingClassWithIndex
diff --git a/test/completion/pep0484_generic_parameters.py b/test/completion/pep0484_generic_parameters.py
index 3898b17f..cbbc4537 100644
--- a/test/completion/pep0484_generic_parameters.py
+++ b/test/completion/pep0484_generic_parameters.py
@@ -6,6 +6,7 @@ from typing import (
     Iterable,
     List,
     Mapping,
+    Optional,
     Tuple,
     Type,
     TypeVar,
@@ -19,7 +20,11 @@ T_co = TypeVar('T_co', covariant=True)
 V = TypeVar('V')
 
 
+just_float = 42.  # type: float
+optional_float = 42.  # type: Optional[float]
 list_of_ints = [42]  # type: List[int]
+list_of_floats = [42.]  # type: List[float]
+list_of_optional_floats = [x or None for x in list_of_floats]  # type: List[Optional[float]]
 list_of_ints_and_strs = [42, 'abc']  # type: List[Union[int, str]]
 
 # Test that simple parameters are handled
@@ -47,6 +52,50 @@ for z in list_t_to_list_t(list_of_ints_and_strs):
 list_of_int_type = [int]  # type: List[Type[int]]
 
 # Test that nested parameters are handled
+def list_optional_t_to_list_t(the_list: List[Optional[T]]) -> List[T]:
+    return [x for x in the_list if x is not None]
+
+
+for xa in list_optional_t_to_list_t(list_of_optional_floats):
+    #? float()
+    xa
+
+# Under covariance rules this is strictly incorrect (because List is mutable,
+# the function would be allowed to put `None`s into our List[float], which would
+# be bad), however we don't expect jedi to enforce that.
+for xa1 in list_optional_t_to_list_t(list_of_floats):
+    #? float()
+    xa1
+
+
+def optional_t_to_list_t(x: Optional[T]) -> List[T]:
+    return [x] if x is not None else []
+
+
+for xb in optional_t_to_list_t(optional_float):
+    #? float()
+    xb
+
+
+for xb2 in optional_t_to_list_t(just_float):
+    #? float()
+    xb2
+
+
+def optional_list_t_to_list_t(x: Optional[List[T]]) -> List[T]:
+    return x if x is not None else []
+
+
+optional_list_float = None  # type: Optional[List[float]]
+for xc in optional_list_t_to_list_t(optional_list_float):
+    #? float()
+    xc
+
+for xc2 in optional_list_t_to_list_t(list_of_floats):
+    #? float()
+    xc2
+
+
 def list_type_t_to_list_t(the_list: List[Type[T]]) -> List[T]:
     return [x() for x in the_list]