diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index 5dfbc7c405bc..049da8a07228 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -945,19 +945,14 @@ def visit_type_type(self, left: TypeType) -> bool:
         return False
 
 
-def is_more_precise(t: Type, s: Type) -> bool:
-    """Check if t is a more precise type than s.
+def is_more_precise(left: Type, right: Type) -> bool:
+    """Check if left is a more precise type than right.
 
-    A t is a proper subtype of s, t is also more precise than s. Also, if
-    s is Any, t is more precise than s for any t. Finally, if t is the same
-    type as s, t is more precise than s.
+    A left is a proper subtype of right, left is also more precise than
+    right. Also, if right is Any, left is more precise than right, for
+    any left.
     """
     # TODO Should List[int] be more precise than List[Any]?
-    if isinstance(s, AnyType):
+    if isinstance(right, AnyType):
         return True
-    if isinstance(s, Instance):
-        if isinstance(t, CallableType):
-            # Fall back to subclass check and ignore other properties of the callable.
-            return is_proper_subtype(t.fallback, s)
-        return is_proper_subtype(t, s)
-    return sametypes.is_same_type(t, s)
+    return is_proper_subtype(left, right)
diff --git a/mypy/test/testtypes.py b/mypy/test/testtypes.py
index f85a9aeb4996..3c7b6189458d 100644
--- a/mypy/test/testtypes.py
+++ b/mypy/test/testtypes.py
@@ -176,11 +176,11 @@ def test_is_more_precise(self) -> None:
         assert_true(is_more_precise(fx.b, fx.anyt))
         assert_true(is_more_precise(self.tuple(fx.b, fx.a),
                                     self.tuple(fx.b, fx.a)))
+        assert_true(is_more_precise(self.tuple(fx.b, fx.b),
+                                    self.tuple(fx.b, fx.a)))
 
         assert_false(is_more_precise(fx.a, fx.b))
         assert_false(is_more_precise(fx.anyt, fx.b))
-        assert_false(is_more_precise(self.tuple(fx.b, fx.b),
-                                     self.tuple(fx.b, fx.a)))
 
     # is_proper_subtype
 
diff --git a/test-data/unit/check-optional.test b/test-data/unit/check-optional.test
index 545df7b31147..138643269e89 100644
--- a/test-data/unit/check-optional.test
+++ b/test-data/unit/check-optional.test
@@ -620,6 +620,20 @@ reveal_type(x) # E: Revealed type is 'Union[builtins.int, builtins.str, builtins
 y: Optional[Union[int, None]]
 reveal_type(y) # E: Revealed type is 'Union[builtins.int, builtins.None]'
 
+[case testOverloadWithNoneAndOptional]
+from typing import overload, Optional
+
+@overload
+def f(x: int) -> str: ...
+@overload
+def f(x: Optional[int]) -> Optional[str]: ...
+def f(x): return x
+
+reveal_type(f(1)) # E: Revealed type is 'builtins.str'
+reveal_type(f(None)) # E: Revealed type is 'Union[builtins.str, builtins.None]'
+x: Optional[int]
+reveal_type(f(x)) # E: Revealed type is 'Union[builtins.str, builtins.None]'
+
 [case testUnionTruthinessTracking]
 from typing import Optional, Any
 def test_or_shortcut(value: Optional[Any]) -> None: