diff --git a/plum/promotion.py b/plum/promotion.py
index 62091e2..1df4a26 100644
--- a/plum/promotion.py
+++ b/plum/promotion.py
@@ -139,8 +139,9 @@ def add_promotion_rule(type1, type2, type_to):
     def rule(t1: type1, t2: type2):
         return type_to
 
-    # If the types are the same, we don't need to add the reverse rule.
-    if type1 is type2:
+    # If the types are the same, we don't need to add the reverse rule. Resolve the
+    # types to handle the case where types are equal, but not identical.
+    if TypeHint(resolve_type_hint(type1)) == TypeHint(resolve_type_hint(type2)):
         return  # Escape early.
 
     @_promotion_rule.dispatch
diff --git a/tests/test_promotion.py b/tests/test_promotion.py
index 12417a2..375e134 100644
--- a/tests/test_promotion.py
+++ b/tests/test_promotion.py
@@ -1,3 +1,5 @@
+import typing
+import warnings
 from numbers import Number
 from typing import Union
 
@@ -159,7 +161,24 @@ def test_inheritance(convert, promote):
     assert promote(Re(), n) == ("Num from Re", n)
     assert promote(Re(), Rat()) == ("Num from Re", "Num from Rat")
 
-    # Test that explicit self-promotion works.
-    # This should also trigger the "escape hatch" in `add_promotion_rule`.
-    add_promotion_rule(Num, Num, Num)
-    assert promote(n, n) == (n, n)
+
+def test_self_promotion(convert, promote):
+    # This should trigger the "escape hatch" in `add_promotion_rule`. It also should not
+    # trigger a redefinition warning. Explicitly test for that.
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+
+        # Simple case where types are identical:
+        add_promotion_rule(Num, Num, Num)
+        n = Num()
+        assert promote(n, n) == (n, n)
+
+        # Also test a more complicated scenario where the types are equal, but not
+        # identical.
+        t1 = typing.Union[int, float]
+        t2 = typing.Union[float, int]
+        assert t1 is not t2
+        add_promotion_rule(t1, t2, str)
+        add_conversion_method(int, str, str)
+        add_conversion_method(float, str, str)
+        assert promote(1, 1.0) == ("1", "1.0")