diff --git a/mypy/applytype.py b/mypy/applytype.py
index d97670034a0bc..997d7ffd3d4dc 100644
--- a/mypy/applytype.py
+++ b/mypy/applytype.py
@@ -3,7 +3,7 @@
 import mypy.subtypes
 from mypy.sametypes import is_same_type
 from mypy.expandtype import expand_type
-from mypy.types import Type, TypeVarId, TypeVarType, CallableType, AnyType
+from mypy.types import Type, TypeVarId, TypeVarType, CallableType, AnyType, PartialType
 from mypy.messages import MessageBuilder
 from mypy.nodes import Context
 
@@ -34,14 +34,15 @@ def apply_generic_arguments(callable: CallableType, types: List[Type],
                        for v1 in type.values):
                     continue
             for value in values:
-                if mypy.subtypes.is_subtype(type, value):
+                if isinstance(type, PartialType) or mypy.subtypes.is_subtype(type, value):
                     types[i] = value
                     break
             else:
                 msg.incompatible_typevar_value(callable, i + 1, type, context)
 
         upper_bound = callable.variables[i].upper_bound
-        if type and not mypy.subtypes.satisfies_upper_bound(type, upper_bound):
+        if (type and not isinstance(type, PartialType) and
+                not mypy.subtypes.satisfies_upper_bound(type, upper_bound)):
             msg.incompatible_typevar_value(callable, i + 1, type, context)
 
     # Create a map from type variable id to target type.
diff --git a/test-data/unit/check-inference.test b/test-data/unit/check-inference.test
index 799fb3525d703..e6b043923a671 100644
--- a/test-data/unit/check-inference.test
+++ b/test-data/unit/check-inference.test
@@ -935,6 +935,15 @@ if A:
 class A: pass
 class B: pass
 
+[case testAssigningAnyStrToNone]
+from typing import Tuple, TypeVar
+AnyStr = TypeVar('AnyStr', str, bytes)
+
+def f(x: AnyStr) -> Tuple[AnyStr]: pass
+x = None
+(x,) = f('')
+reveal_type(x)  # E: Revealed type is 'builtins.str'
+
 
 -- Inferring attribute types
 -- -------------------------