diff --git a/test/command_checker/add_reference_test.rb b/test/command_checker/add_reference_test.rb
index 2db919f..5f1d4e7 100644
--- a/test/command_checker/add_reference_test.rb
+++ b/test/command_checker/add_reference_test.rb
@@ -138,6 +138,30 @@ def test_add_reference_foreign_key_no_validate
       assert_safe AddReferenceForeignKeyNoValidate
     end
 
+    def test_add_reference_foreign_key_no_validate_is_not_idempotent
+      assert_empty @connection.foreign_keys(:projects)
+
+      migrate AddReferenceForeignKeyNoValidate
+      assert_raises_with_message(StandardError, /column "user_id" of relation "projects" already exists/) do
+        migrate AddReferenceForeignKeyNoValidate
+      end
+    ensure
+      migrate AddReferenceForeignKeyNoValidate, direction: :down
+      assert_empty @connection.foreign_keys(:projects)
+    end
+
+    class AddReferenceForeignKeyNoValidatePluralizeName < TestMigration
+      disable_ddl_transaction!
+
+      def change
+        add_reference :projects, :users, index: false, foreign_key: { validate: false }
+      end
+    end
+
+    def test_add_reference_foreign_key_no_validate_with_pluralized_table_name
+      assert_safe AddReferenceForeignKeyNoValidatePluralizeName
+    end
+
     class AddReferenceForeignKeyValidate < TestMigration
       def change
         add_reference :projects, :user, index: false, foreign_key: { validate: true }
diff --git a/test/command_checker/foreign_keys_test.rb b/test/command_checker/foreign_keys_test.rb
index 4b7a560..6ee363e 100644
--- a/test/command_checker/foreign_keys_test.rb
+++ b/test/command_checker/foreign_keys_test.rb
@@ -69,6 +69,31 @@ def test_add_foreign_key_no_validate
       assert_safe AddForeignKeyNoValidate
     end
 
+    def test_add_foreign_key_no_validate_is_idempotent
+      assert_empty @connection.foreign_keys(:projects)
+
+      migrate AddForeignKeyNoValidate
+      migrate AddForeignKeyNoValidate
+      migrate AddForeignKeyNoValidate
+      
+      assert_equal 1, @connection.foreign_keys(:projects).size
+    ensure
+      migrate AddForeignKeyNoValidate, direction: :down
+      assert_empty @connection.foreign_keys(:projects)
+    end
+
+    class AddForeignKeySingularToTable < TestMigration
+      def change
+        add_foreign_key :projects, :user, validate: false
+      end
+    end
+
+    def test_add_foreign_key_no_validate
+      assert_raises_with_message(StandardError, /PG::UndefinedTable: ERROR:  relation "user" does not exist/i) do
+        assert_safe AddForeignKeySingularToTable
+      end
+    end
+
     class AddForeignKeyFromNewTable < TestMigration
       def change
         create_table :posts_new do |t|
diff --git a/test/schema_statements/add_reference_concurrently_test.rb b/test/schema_statements/add_reference_concurrently_test.rb
index 7f4cf8d..459f9ad 100644
--- a/test/schema_statements/add_reference_concurrently_test.rb
+++ b/test/schema_statements/add_reference_concurrently_test.rb
@@ -71,6 +71,35 @@ def test_add_reference_concurrently_with_foreign_key
       end
     end
 
+    def test_add_reference_concurrently_with_foreign_key_is_idempotent
+      assert_empty @connection.foreign_keys(:projects)
+
+      connection.add_reference_concurrently :milestones, :project, foreign_key: true
+      connection.add_reference_concurrently :milestones, :project, foreign_key: true
+      connection.add_reference_concurrently :milestones, :project, foreign_key: true
+
+      assert_equal 1, @connection.foreign_keys(:projects).size
+    end
+
+    def test_add_reference_concurrently_with_foreign_key_with_pluralized_table_name
+      assert_sql(
+        'REFERENCES "projects" ("id") NOT VALID',
+        'ALTER TABLE "milestones" VALIDATE CONSTRAINT'
+      ) do
+        connection.add_reference_concurrently :milestones, :projects, foreign_key: true
+      end
+    end
+
+    def test_add_reference_concurrently_with_foreign_key_is_idempotent_with_pluralized_table_name
+      assert_empty @connection.foreign_keys(:projects)
+
+      connection.add_reference_concurrently :milestones, :projects, foreign_key: true
+      connection.add_reference_concurrently :milestones, :projects, foreign_key: true
+      connection.add_reference_concurrently :milestones, :projects, foreign_key: true
+
+      assert_equal 1, @connection.foreign_keys(:projects).size
+    end
+
     def test_add_reference_concurrently_with_unvalidated_foreign_key
       refute_sql("VALIDATE CONSTRAINT") do
         connection.add_reference_concurrently :milestones, :project, foreign_key: { validate: false }