diff --git a/tests/adapter/dbt/tests/adapter/constraints/test_constraints.py b/tests/adapter/dbt/tests/adapter/constraints/test_constraints.py
index 49e78d19a34..de78143aff7 100644
--- a/tests/adapter/dbt/tests/adapter/constraints/test_constraints.py
+++ b/tests/adapter/dbt/tests/adapter/constraints/test_constraints.py
@@ -228,7 +228,8 @@ def test__constraints_ddl(self, project, expected_sql):
         )
 
         results = run_dbt(["run", "-s", "+my_model"])
-        assert len(results) == 2
+        # assert at least my_model was run - additional upstreams may or may not be provided to the test setup via models fixture
+        assert len(results) >= 1
 
         # grab the sql and replace the model identifier to make it generic for all adapters
         # the name is not what we're testing here anyways and varies based on materialization
@@ -481,7 +482,8 @@ def test__model_constraints_ddl(self, project, expected_sql):
         )
 
         results = run_dbt(["run", "-s", "+my_model"])
-        assert len(results) == 2
+        # assert at least my_model was run - additional upstreams may or may not be provided to the test setup via models fixture
+        assert len(results) >= 1
         generated_sql = read_file("target", "run", "test", "models", "my_model.sql")
         generated_sql_modified = _normalize_whitespace(generated_sql)
         generated_sql_generic = _find_and_replace(