diff --git a/mypy/checker.py b/mypy/checker.py
index 95789831fd6f..376d84cbcac0 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -4802,7 +4802,15 @@ def refine_identity_comparison_expression(self,
         """
         should_coerce = True
         if coerce_only_in_literal_context:
-            should_coerce = any(is_literal_type_like(operand_types[i]) for i in chain_indices)
+
+            def should_coerce_inner(typ: Type) -> bool:
+                typ = get_proper_type(typ)
+                return is_literal_type_like(typ) or (
+                    isinstance(typ, Instance)
+                    and typ.type.is_enum
+                )
+
+            should_coerce = any(should_coerce_inner(operand_types[i]) for i in chain_indices)
 
         target: Optional[Type] = None
         possible_target_indices = []
diff --git a/test-data/unit/check-narrowing.test b/test-data/unit/check-narrowing.test
index d6b25ef456d9..5651ac7d5d90 100644
--- a/test-data/unit/check-narrowing.test
+++ b/test-data/unit/check-narrowing.test
@@ -699,47 +699,47 @@ class FlipFlopStr:
     def mutate(self) -> None:
         self.state = "state-2" if self.state == "state-1" else "state-1"
 
-def test1(switch: FlipFlopEnum) -> None:
+
+def test1(switch: FlipFlopStr) -> None:
     # Naively, we might assume the 'assert' here would narrow the type to
-    # Literal[State.A]. However, doing this ends up breaking a fair number of real-world
+    # Literal["state-1"]. However, doing this ends up breaking a fair number of real-world
     # code (usually test cases) that looks similar to this function: e.g. checks
     # to make sure a field was mutated to some particular value.
     #
     # And since mypy can't really reason about state mutation, we take a conservative
     # approach and avoid narrowing anything here.
 
-    assert switch.state == State.A
-    reveal_type(switch.state)          # N: Revealed type is "__main__.State"
+    assert switch.state == "state-1"
+    reveal_type(switch.state)          # N: Revealed type is "builtins.str"
 
     switch.mutate()
 
-    assert switch.state == State.B
-    reveal_type(switch.state)          # N: Revealed type is "__main__.State"
+    assert switch.state == "state-2"
+    reveal_type(switch.state)          # N: Revealed type is "builtins.str"
 
 def test2(switch: FlipFlopEnum) -> None:
-    # So strictly speaking, we ought to do the same thing with 'is' comparisons
-    # for the same reasons as above. But in practice, not too many people seem to
-    # know that doing 'some_enum is MyEnum.Value' is idiomatic. So in practice,
-    # this is probably good enough for now.
+    # This is the same thing as 'test1', except we use enums, which we allow to be narrowed
+    # to literals.
 
-    assert switch.state is State.A
+    assert switch.state == State.A
     reveal_type(switch.state)          # N: Revealed type is "Literal[__main__.State.A]"
 
     switch.mutate()
 
-    assert switch.state is State.B     # E: Non-overlapping identity check (left operand type: "Literal[State.A]", right operand type: "Literal[State.B]")
+    assert switch.state == State.B     # E: Non-overlapping equality check (left operand type: "Literal[State.A]", right operand type: "Literal[State.B]")
     reveal_type(switch.state)          # E: Statement is unreachable
 
-def test3(switch: FlipFlopStr) -> None:
-    # This is the same thing as 'test1', except we try using str literals.
+def test3(switch: FlipFlopEnum) -> None:
+    # Same thing, but using 'is' comparisons. Previously mypy's behaviour differed
+    # here, narrowing when using 'is', but not when using '=='.
 
-    assert switch.state == "state-1"
-    reveal_type(switch.state)          # N: Revealed type is "builtins.str"
+    assert switch.state is State.A
+    reveal_type(switch.state)          # N: Revealed type is "Literal[__main__.State.A]"
 
     switch.mutate()
 
-    assert switch.state == "state-2"
-    reveal_type(switch.state)          # N: Revealed type is "builtins.str"
+    assert switch.state is State.B     # E: Non-overlapping identity check (left operand type: "Literal[State.A]", right operand type: "Literal[State.B]")
+    reveal_type(switch.state)          # E: Statement is unreachable
 [builtins fixtures/primitives.pyi]
 
 [case testNarrowingEqualityRequiresExplicitStrLiteral]
@@ -791,6 +791,7 @@ reveal_type(x_union)      # N: Revealed type is "Union[Literal['A'], Literal['B'
 
 [case testNarrowingEqualityRequiresExplicitEnumLiteral]
 # flags: --strict-optional
+from typing import Union
 from typing_extensions import Literal, Final
 from enum import Enum
 
@@ -801,19 +802,19 @@ class Foo(Enum):
 A_final: Final = Foo.A
 A_literal: Literal[Foo.A]
 
-# See comments in testNarrowingEqualityRequiresExplicitStrLiteral and
-# testNarrowingEqualityFlipFlop for more on why we can't narrow here.
+# Note this is unlike testNarrowingEqualityRequiresExplicitStrLiteral
+# See also testNarrowingEqualityFlipFlop
 x1: Foo
 if x1 == Foo.A:
-    reveal_type(x1)  # N: Revealed type is "__main__.Foo"
+    reveal_type(x1)  # N: Revealed type is "Literal[__main__.Foo.A]"
 else:
-    reveal_type(x1)  # N: Revealed type is "__main__.Foo"
+    reveal_type(x1)  # N: Revealed type is "Literal[__main__.Foo.B]"
 
 x2: Foo
 if x2 == A_final:
-    reveal_type(x2)  # N: Revealed type is "__main__.Foo"
+    reveal_type(x2)  # N: Revealed type is "Literal[__main__.Foo.A]"
 else:
-    reveal_type(x2)  # N: Revealed type is "__main__.Foo"
+    reveal_type(x2)  # N: Revealed type is "Literal[__main__.Foo.B]"
 
 # But we let this narrow since there's an explicit literal in the RHS.
 x3: Foo
@@ -821,6 +822,14 @@ if x3 == A_literal:
     reveal_type(x3)  # N: Revealed type is "Literal[__main__.Foo.A]"
 else:
     reveal_type(x3)  # N: Revealed type is "Literal[__main__.Foo.B]"
+
+
+class SingletonFoo(Enum):
+    A = "A"
+
+def bar(x: Union[SingletonFoo, Foo], y: SingletonFoo) -> None:
+    if x == y:
+        reveal_type(x)  # N: Revealed type is "Literal[__main__.SingletonFoo.A]"
 [builtins fixtures/primitives.pyi]
 
 [case testNarrowingEqualityDisabledForCustomEquality]