diff --git a/django/db/backends/base/schema.py b/django/db/backends/base/schema.py
index 896ea3d517..412fb46f16 100644
--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -1155,8 +1155,10 @@ class BaseDatabaseSchemaEditor:
         return not old_field.primary_key and new_field.primary_key
 
     def _unique_should_be_added(self, old_field, new_field):
-        return (not old_field.unique and new_field.unique) or (
-            old_field.primary_key and not new_field.primary_key and new_field.unique
+        return (
+            not new_field.primary_key and
+            new_field.unique and
+            (not old_field.unique or old_field.primary_key)
         )
 
     def _rename_field_sql(self, table, old_field, new_field, new_type):
diff --git a/django/db/backends/oracle/schema.py b/django/db/backends/oracle/schema.py
index 0d1c7f5d4b..47d60ea290 100644
--- a/django/db/backends/oracle/schema.py
+++ b/django/db/backends/oracle/schema.py
@@ -174,12 +174,6 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
             return False
         return create_index
 
-    def _unique_should_be_added(self, old_field, new_field):
-        return (
-            super()._unique_should_be_added(old_field, new_field) and
-            not self._field_became_primary_key(old_field, new_field)
-        )
-
     def _is_identity_column(self, table_name, column_name):
         with self.connection.cursor() as cursor:
             cursor.execute("""
diff --git a/tests/schema/tests.py b/tests/schema/tests.py
index 9e23c4608e..b8ad08239b 100644
--- a/tests/schema/tests.py
+++ b/tests/schema/tests.py
@@ -741,6 +741,13 @@ class SchemaTests(TransactionTestCase):
         with connection.schema_editor() as editor:
             editor.remove_field(Author, Author._meta.get_field('id'))
             editor.alter_field(Author, old_field, new_field, strict=True)
+        # Redundant unique constraint is not added.
+        count = self.get_constraints_count(
+            Author._meta.db_table,
+            Author._meta.get_field('uuid').column,
+            None,
+        )
+        self.assertLessEqual(count['uniques'], 1)
 
     @isolate_apps('schema')
     def test_alter_primary_key_quoted_db_table(self):