diff --git a/mypy/types.py b/mypy/types.py
index b97937526ae4..1952585d58dd 100644
--- a/mypy/types.py
+++ b/mypy/types.py
@@ -858,9 +858,6 @@ def make_simplified_union(items: List[Type], line: int = -1, column: int = -1) -
                     all_items.append(typ)
             items = all_items
 
-        if any(isinstance(typ, AnyType) for typ in items):
-            return AnyType()
-
         from mypy.subtypes import is_subtype
         removed = set()  # type: Set[int]
         for i, ti in enumerate(items):
@@ -868,7 +865,11 @@ def make_simplified_union(items: List[Type], line: int = -1, column: int = -1) -
             # Keep track of the truishness info for deleted subtypes which can be relevant
             cbt = cbf = False
             for j, tj in enumerate(items):
-                if i != j and is_subtype(tj, ti):
+                # Attempt to only combine true subtypes by avoiding types containing Any.
+                # TODO: Properly exclude generics and functions.
+                tj_is_anylike = (isinstance(tj, AnyType) or
+                                 (isinstance(tj, Instance) and tj.type.fallback_to_any))
+                if i != j and is_subtype(tj, ti) and not tj_is_anylike:
                     removed.add(j)
                     cbt = cbt or tj.can_be_true
                     cbf = cbf or tj.can_be_false
diff --git a/test-data/unit/check-optional.test b/test-data/unit/check-optional.test
index 010ab8f9eef5..4b8f3104256d 100644
--- a/test-data/unit/check-optional.test
+++ b/test-data/unit/check-optional.test
@@ -428,3 +428,10 @@ x + 1
 [out]
 main:2: note: In module imported here:
 tmp/a.py:3: error: Unsupported left operand type for + (some union)
+
+[case testOptionalFallbackToNone]
+from typing import Any, Optional
+class C(Any):
+    pass
+x = None  # type: Optional[C]
+x.foo()  # E: Some element of union has no attribute "foo"