diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
index 872684db4df7..96f2e1e711e2 100644
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -1090,6 +1090,17 @@ def check_boolean_op(self, e: OpExpr, context: Context) -> Type:
                 mypy.checker.find_isinstance_check(e.left, self.chk.type_map,
                                                    self.chk.typing_mode_weak())
         elif e.op == 'or':
+            # Special case for `Optional[T] or T` -- this should infer T.
+            # If the type is a Union containing None, remove the None.
+            if isinstance(left_type, UnionType):
+                items = [i for i in left_type.items if not isinstance(i, NoneTyp)]
+                if len(items) < len(left_type.items):
+                    left_type = UnionType.make_simplified_union(items)
+
+            # Special case for `None or T` -- this should infer T.
+            if isinstance(left_type, NoneTyp):
+                left_type = None
+
             _, right_map = \
                 mypy.checker.find_isinstance_check(e.left, self.chk.type_map,
                                                    self.chk.typing_mode_weak())
@@ -1103,9 +1114,13 @@ def check_boolean_op(self, e: OpExpr, context: Context) -> Type:
 
             right_type = self.accept(e.right, left_type)
 
-        self.check_not_void(left_type, context)
+        if left_type is not None:
+            self.check_not_void(left_type, context)
         self.check_not_void(right_type, context)
-        return UnionType.make_simplified_union([left_type, right_type])
+        if left_type is None:
+            return right_type
+        else:
+            return UnionType.make_simplified_union([left_type, right_type])
 
     def check_list_multiply(self, e: OpExpr) -> Type:
         """Type check an expression of form '[...] * e'.
diff --git a/test-data/unit/check-optional.test b/test-data/unit/check-optional.test
index 9e842d38aafc..d63dcebe419a 100644
--- a/test-data/unit/check-optional.test
+++ b/test-data/unit/check-optional.test
@@ -175,3 +175,68 @@ def f(x: None) -> str: pass
 def f(x: int) -> int: pass
 reveal_type(f(None))  # E: Revealed type is 'builtins.str'
 reveal_type(f(0))  # E: Revealed type is 'builtins.int'
+
+[case testOptionalTypeOrTypePlain]
+from typing import Optional
+def f(a: Optional[int]) -> int:
+    return a or 0
+[out]
+
+[case testOptionalTypeOrTypeTypeVar]
+from typing import Optional, TypeVar
+T = TypeVar('T')
+def f(a: Optional[T], b: T) -> T:
+    return a or b
+[out]
+
+[case testOptionalTypeOrTypeBothOptional]
+from typing import Optional
+def f(a: Optional[int], b: Optional[int]) -> None:
+    reveal_type(a or b)
+def g(a: int, b: Optional[int]) -> None:
+    reveal_type(a or b)
+[out]
+main: note: In function "f":
+main:3: error: Revealed type is 'Union[builtins.int, builtins.None]'
+main: note: In function "g":
+main:5: error: Revealed type is 'Union[builtins.int, builtins.None]'
+
+[case testOptionalTypeOrTypeComplexUnion]
+from typing import Union
+def f(a: Union[int, str, None]) -> None:
+    reveal_type(a or 'default')
+[out]
+main: note: In function "f":
+main:3: error: Revealed type is 'Union[builtins.int, builtins.str]'
+
+[case testOptionalTypeOrTypeNoTriggerPlain]
+from typing import Optional
+def f(a: Optional[int], b: int) -> int:
+    return b or a
+[out]
+main: note: In function "f":
+main:3: error: Incompatible return value type (got "Optional[int]", expected "int")
+
+[case testOptionalTypeOrTypeNoTriggerTypeVar]
+from typing import Optional, TypeVar
+T = TypeVar('T')
+def f(a: Optional[T], b: T) -> T:
+    return b or a
+[out]
+main: note: In function "f":
+main:4: error: Incompatible return value type (got "Optional[T]", expected "T")
+
+[case testNoneOrStringIsString]
+def f() -> str:
+    a = None
+    b = ''
+    return a or b
+[out]
+
+[case testNoneOrTypeVarIsTypeVar]
+from typing import TypeVar
+T = TypeVar('T')
+def f(b: T) -> T:
+    a = None
+    return a or b
+[out]