diff --git a/tests/relational/test_train_synthetics.py b/tests/relational/test_train_synthetics.py
index ccbb784b..f805aa26 100644
--- a/tests/relational/test_train_synthetics.py
+++ b/tests/relational/test_train_synthetics.py
@@ -76,6 +76,28 @@ def test_train_synthetics_multiple_calls_additive(ecom, tmpdir):
     assert set(mt._synthetics_train.models.keys()) == {"products", "users"}
 
 
+def test_train_synthetics_models_for_dbs_with_invented_tables(documents, tmpdir):
+    mt = MultiTable(documents, project_display_name=tmpdir)
+    mt.train_synthetics()
+
+    assert set(mt._synthetics_train.models.keys()) == {
+        "users",
+        "payments",
+        "purchases-sfx",
+        "purchases-data-years-sfx",
+    }
+
+
+def test_train_synthetics_table_filters_cascade_to_invented_tables(documents, tmpdir):
+    # When a user provides the ("public") name of a table that contained JSON and led
+    # to the creation of invented tables, we recognize that as implicitly applying to
+    # all the tables internally created from that source table.
+    mt = MultiTable(documents, project_display_name=tmpdir)
+    mt.train_synthetics(ignore={"purchases"})
+
+    assert set(mt._synthetics_train.models.keys()) == {"users", "payments"}
+
+
 def test_train_synthetics_multiple_calls_overwrite(ecom, tmpdir, project):
     project.create_model_obj.return_value = "m1"