# django__django-12708
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on the issue description and the architect's analysis, I need to generate a patch for the Django `_delete_composed_index()` method. The bug is that when deleting an `index_together`, the method finds both the unique constraint and the index constraint because they share the same columns. The fix needs to filter by constraint type.

Here's the patch:

```
--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -355,7 +355,7 @@ class BaseDatabaseSchemaEditor:
         self.execute(self._delete_constraint_sql(self.sql_delete_pk, model, pk_names[0]))
         return True
 
-    def _delete_composed_index(self, model, fields, constraint_kwargs, sql):
+    def _delete_composed_index(self, model, fields, constraint_kwargs, sql, exclude_unique=False):
         columns = [model._meta.get_field(field).column for field in fields]
         constraint_names = self._constraint_names(model, columns, **constraint_kwargs)
         if len(constraint_names) != 1:
@@ -375,7 +375,14 @@ class BaseDatabaseSchemaEditor:
     def alter_index_together(self, model, old_index_together, new_index_together):
         olds = {tuple(fields) for fields in old_index_together}
         news = {tuple(fields) for fields in new_index_together}
-        # Deleted indexes
+        # Deleted indexes. When removing an index, exclude unique constraints
+        # from consideration since the same columns might have both
+        # index_together and unique_together defined.
         for fields in olds.difference(news):
-            self._delete_composed_index(model, fields, {'index': True}, self.sql_delete_index)
+            self._delete_composed_index(
+                model,
+                fields,
+                {'index': True, 'unique': False},
+                self.sql_delete_index,
+            )
         # Created indexes
         for fields in news.difference(olds):
             self._create_index(model, fields, suffix='_idx')
```

Wait, let me reconsider. The issue is in `_constraint_names` which needs to filter properly. Let me provide a more targeted fix based on the actual Django codebase structure:

--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -375,8 +375,12 @@ class BaseDatabaseSchemaEditor:
     def alter_index_together(self, model, old_index_together, new_index_together):
         olds = {tuple(fields) for fields in old_index_together}
         news = {tuple(fields) for fields in new_index_together}
-        # Deleted indexes
+        # Deleted indexes. When removing an index, exclude unique constraints
+        # from consideration since the same columns might have both
+        # index_together and unique_together defined.
         for fields in olds.difference(news):
-            self._delete_composed_index(model, fields, {'index': True}, self.sql_delete_index)
+            self._delete_composed_index(
+                model, fields, {'index': True, 'unique': False}, self.sql_delete_index
+            )
         # Created indexes
         for fields in news.difference(olds):
             self._create_index(model, fields, suffix='_idx')