diff --git a/mypy/join.py b/mypy/join.py
index 7489fec2572e..3adb9531e5a2 100644
--- a/mypy/join.py
+++ b/mypy/join.py
@@ -87,7 +87,7 @@ def visit_union_type(self, t: UnionType) -> Type:
         if is_subtype(self.s, t):
             return t
         else:
-            return UnionType(t.items + [self.s])
+            return UnionType.make_simplified_union([self.s, t])
 
     def visit_error_type(self, t: ErrorType) -> Type:
         return t
@@ -235,7 +235,6 @@ def join_instances(t: Instance, s: Instance) -> Type:
 
     Return ErrorType if the result is ambiguous.
     """
-
     if t.type == s.type:
         # Simplest case: join two types with the same base type (but
         # potentially different arguments).
@@ -264,16 +263,29 @@ def join_instances_via_supertype(t: Instance, s: Instance) -> Type:
         return join_types(t.type._promote, s)
     elif s.type._promote and is_subtype(s.type._promote, t):
         return join_types(t, s.type._promote)
-    res = s
-    mapped = map_instance_to_supertype(t, t.type.bases[0].type)
-    join = join_instances(mapped, res)
-    # If the join failed, fail. This is a defensive measure (this might
-    # never happen).
-    if isinstance(join, ErrorType):
-        return join
-    # Now the result must be an Instance, so the cast below cannot fail.
-    res = cast(Instance, join)
-    return res
+    # Compute the "best" supertype of t when joined with s.
+    # The definition of "best" may evolve; for now it is the one with
+    # the longest MRO.  Ties are broken by using the earlier base.
+    best = None  # type: Type
+    for base in t.type.bases:
+        mapped = map_instance_to_supertype(t, base.type)
+        res = join_instances(mapped, s)
+        if best is None or is_better(res, best):
+            best = res
+    assert best is not None
+    return best
+
+
+def is_better(t: Type, s: Type) -> bool:
+    # Given two possible results from join_instances_via_supertype(),
+    # indicate whether t is the better one.
+    if isinstance(t, Instance):
+        if not isinstance(s, Instance):
+            return True
+        # Use len(mro) as a proxy for the better choice.
+        if len(t.type.mro) > len(s.type.mro):
+            return True
+    return False
 
 
 def is_similar_callables(t: CallableType, s: CallableType) -> bool:
diff --git a/mypy/test/data/check-inference.test b/mypy/test/data/check-inference.test
index 999b1cb8e054..50df29d3a024 100644
--- a/mypy/test/data/check-inference.test
+++ b/mypy/test/data/check-inference.test
@@ -599,9 +599,9 @@ g(a)
 b = f(A(), B())
 g(b)
 c = f(A(), D())
-g(c) # E: Argument 1 to "g" has incompatible type "object"; expected "I"
+g(c) # E: Argument 1 to "g" has incompatible type "J"; expected "I"
 d = f(D(), A())
-g(d) # E: Argument 1 to "g" has incompatible type "object"; expected "I"
+g(d) # E: Argument 1 to "g" has incompatible type "J"; expected "I"
 e = f(D(), C())
 g(e) # E: Argument 1 to "g" has incompatible type "object"; expected "I"
 
@@ -646,9 +646,9 @@ def f(a: T, b: T) -> T: pass
 def g(x: K) -> None: pass
 
 a = f(B(), C())
-g(a) # E: Argument 1 to "g" has incompatible type "object"; expected "K"
+g(a) # E: Argument 1 to "g" has incompatible type "J"; expected "K"
 b = f(A(), C())
-g(b) # E: Argument 1 to "g" has incompatible type "object"; expected "K"
+g(b) # E: Argument 1 to "g" has incompatible type "J"; expected "K"
 c = f(A(), B())
 g(c)
 
@@ -1593,3 +1593,49 @@ tmp/m.py: note: In function "g":
 tmp/m.py:2: error: "int" not callable
 main: note: In function "f":
 main:3: error: "int" not callable
+
+
+-- Tests for special cases of unification
+-- --------------------------------------
+
+[case testUnificationRedundantUnion]
+from typing import Union
+a = None  # type: Union[int, str]
+b = None  # type: Union[str, tuple]
+def f(): pass
+def g(x: Union[int, str]): pass
+c = a if f() else b
+g(c) # E: Argument 1 to "g" has incompatible type "Union[int, str, tuple]"; expected "Union[int, str]"
+
+[case testUnificationMultipleInheritance]
+class A: pass
+class B:
+    def foo(self): pass
+class C(A, B): pass
+def f(): pass
+a1 = B() if f() else C()
+a1.foo()
+a2 = C() if f() else B()
+a2.foo()
+
+[case testUnificationMultipleInheritanceAmbiguous]
+# Show that join_instances_via_supertype() breakes ties using the first base class.
+class A1: pass
+class B1:
+    def foo1(self): pass
+class C1(A1, B1): pass
+
+class A2: pass
+class B2:
+    def foo2(self): pass
+class C2(A2, B2): pass
+
+class D1(C1, C2): pass
+class D2(C2, C1): pass
+
+def f(): pass
+
+a1 = D1() if f() else D2()
+a1.foo1()
+a2 = D2() if f() else D1()
+a2.foo2()