diff --git a/django/db/migrations/operations/models.py b/django/db/migrations/operations/models.py
index 967a91fdc8..b89b6b511b 100644
--- a/django/db/migrations/operations/models.py
+++ b/django/db/migrations/operations/models.py
@@ -861,6 +861,11 @@ class AddIndex(IndexOperation):
     def migration_name_fragment(self):
         return "%s_%s" % (self.model_name_lower, self.index.name.lower())
 
+    def reduce(self, operation, app_label):
+        if isinstance(operation, RemoveIndex) and self.index.name == operation.name:
+            return []
+        return super().reduce(operation, app_label)
+
 
 class RemoveIndex(IndexOperation):
     """Remove an index from a model."""
diff --git a/tests/migrations/test_optimizer.py b/tests/migrations/test_optimizer.py
index 8cd4c67fbd..2f6616ad5b 100644
--- a/tests/migrations/test_optimizer.py
+++ b/tests/migrations/test_optimizer.py
@@ -1158,3 +1158,17 @@ class OptimizerTests(SimpleTestCase):
                 ),
             ]
         )
+
+    def test_add_remove_index(self):
+        self.assertOptimizesTo(
+            [
+                migrations.AddIndex(
+                    "Pony",
+                    models.Index(
+                        fields=["weight", "pink"], name="idx_pony_weight_pink"
+                    ),
+                ),
+                migrations.RemoveIndex("Pony", "idx_pony_weight_pink"),
+            ],
+            [],
+        )