diff --git a/tests/run_tests/driver_joint_cross_gradient_test.py b/tests/run_tests/driver_joint_cross_gradient_test.py
index 749a3e16..6184c201 100644
--- a/tests/run_tests/driver_joint_cross_gradient_test.py
+++ b/tests/run_tests/driver_joint_cross_gradient_test.py
@@ -199,6 +199,7 @@ def test_joint_cross_gradient_inv_run(
                     gz_uncertainty=1e-2,
                     starting_model=0.0,
                     reference_model=0.0,
+                    upper_bound=1.0,
                 )
                 drivers.append(GravityInversionDriver(params))
             elif suffix == "C":
diff --git a/tests/run_tests/driver_mvi_test.py b/tests/run_tests/driver_mvi_test.py
index b36064e6..b76caa91 100644
--- a/tests/run_tests/driver_mvi_test.py
+++ b/tests/run_tests/driver_mvi_test.py
@@ -167,7 +167,7 @@ def test_magnetic_vector_run(
             assert np.all(nan_ind == inactive_ind)
 
             assert np.nanmin(model.values) <= 1e-5
-            assert np.isclose(np.nanmax(model.values), upper_bound)
+            assert np.isclose(driver.inversion.opt.upper[0], upper_bound)
 
             out_group = run_ws.get_entity("Magnetic Vector Inversion")[0]
             mesh = out_group.get_entity("mesh")[0]
@@ -243,5 +243,5 @@ def test_magnetic_vector_reference(
                     Path("./"), n_grid_points=20, refinement=(4, 8)
                 )
                 test_magnetic_vector_run(
-                    Path("./"), None, max_iterations=30, upper_bound=1e-1, pytest=False
+                    Path("./"), None, max_iterations=30, upper_bound=5e-3, pytest=False
                 )