diff --git a/jass/test/test_init_table.py b/jass/test/test_init_table.py
index e790689b9dfc8672cf6c016d86c990fa76cfc73d..3d7b0ef77d96b29fa17daef24032b2fd5c8de1df 100644
--- a/jass/test/test_init_table.py
+++ b/jass/test/test_init_table.py
@@ -19,10 +19,13 @@ class TestInitTable(object):
         # Create a temporary directory
         self.test_dir = tempfile.mkdtemp()
         input_data_path = self.get_file_path_fn("*chr*.txt")
-        init_covariance_path = self.get_file_path_fn("COV.csv")
+        if self.computed_cov:
+            init_covariance_path = None
+        else:
+            init_covariance_path = self.get_file_path_fn("COV.csv")
         regions_map_path = self.get_file_path_fn("regions.txt")
         description_file_path = self.get_file_path_fn("summary.csv")
-        self.expected_hdf_path = self.get_file_path_fn("initTable.hdf5")
+        self.expected_hdf_path = self.get_file_path_fn(f"initTable{'-computed-cov' if self.computed_cov else ''}.hdf5")
         init_table_path = os.path.join(self.test_dir, "test_init_table.hdf5")
         create_inittable_file(
             input_data_path,
@@ -66,15 +69,15 @@ class TestInitTable(object):
         assert_frame_equal(self.expected_cov, self.result_cov, check_like=True)
 
 
-params = [("nonans", "data_test1"), ("withnans", "data_test2")]
+params = [("nonans", "data_real", True), ("withnans", "data_real", False)]
 
-for name, param in params:
+for name, param, computed_cov in params:
     cls_name = "TestInitTable_%s" % (name,)
     print(cls_name)
     globals()[cls_name] = type(
         cls_name,
         (TestInitTable, JassTestCase),
-        {"test_folder": param, "__test__": True},
+        {"test_folder": param, "computed_cov":computed_cov, "__test__": True},
     )
 
 if __name__ == "__main__":