diff --git a/Wrappers/Python/test/test_BlockOperator.py b/Wrappers/Python/test/test_BlockOperator.py
index 3e81ab4cad..bff62cd5af 100644
--- a/Wrappers/Python/test/test_BlockOperator.py
+++ b/Wrappers/Python/test/test_BlockOperator.py
@@ -26,7 +26,7 @@
 from cil.framework import ImageGeometry, ImageData
 import numpy
 from cil.optimisation.operators import FiniteDifferenceOperator
-
+from cil.optimisation.operators import LinearOperator
 initialise_tests()
 
 class TestBlockOperator(unittest.TestCase):
@@ -187,9 +187,9 @@ def test_FiniteDiffOperator(self):
         G = FiniteDifferenceOperator(ig, direction=0, bnd_cond = 'Neumann')
         logging.info("{} {}".format(type(u), str(u.as_array())))    
         logging.info(str(G.direct(u).as_array()))
-
+        LinearOperator.PowerMethod(G, range_is_domain=False)
         # Gradient Operator norm, for one direction should be close to 2
-        numpy.testing.assert_allclose(G.norm(), numpy.sqrt(4), atol=0.1)
+        numpy.testing.assert_allclose(LinearOperator.PowerMethod(G, range_is_domain=False), numpy.sqrt(4), atol=0.1)
 
         M1, N1, K1 = 200, 300, 2
         ig1 = ImageGeometry(voxel_num_x = M1, voxel_num_y = N1, channels = K1)
diff --git a/Wrappers/Python/test/test_Operator.py b/Wrappers/Python/test/test_Operator.py
index 4d2cf5c1e4..ea756157d6 100644
--- a/Wrappers/Python/test/test_Operator.py
+++ b/Wrappers/Python/test/test_Operator.py
@@ -306,25 +306,32 @@ def test_PowerMethod(self):
         numpy.testing.assert_almost_equal(res1,3.1624439599276974, decimal=4) 
 
         # 2x2 non-diagonalisable nilpotent matrix
-        with self.assertRaises(ValueError):
-            
-            M1=numpy.array([[0.,1.], [0.,0.]])
-            M1op = MatrixOperator(M1)
-            res1 = M1op.PowerMethod(M1op,5)
-            
+        M1=numpy.array([[0.,1.], [0.,0.]])
+        M1op = MatrixOperator(M1)
+        res1 = M1op.PowerMethod(M1op,5)
+        numpy.testing.assert_almost_equal(res1,0, decimal=4) 
+
+        # 2x2 non-diagonalisable nilpotent matrix where range_is_domain is False
+        M1=numpy.array([[0.,1.], [0.,0.]])
+        M1op = MatrixOperator(M1)
+        res1 = M1op.PowerMethod(M1op,5, range_is_domain=False)
+        numpy.testing.assert_almost_equal(res1,1, decimal=4) 
+
+
         # 2x2 matrix, max absolute eigenvalue is not unique and initial vector chosen for non-convergence
-        with self.assertWarns(Warning):
-            M1=numpy.array([[2.,1.], [0.,-2.]])
-            M1op = MatrixOperator(M1)
-            res1 = M1op.PowerMethod(M1op,100, initial=DataContainer(numpy.array([1.,1.])))
+        
+        M1=numpy.array([[2.,1.], [0.,-2.]])
+        M1op = MatrixOperator(M1)
+        _,_,_,_,convergence = M1op.PowerMethod(M1op,100, initial=DataContainer(numpy.array([1.,1.])), return_all=True)
+        numpy.testing.assert_equal(convergence,False) 
 
         # 2x2 matrix, max absolute eigenvalue is not unique and initial vector chosen for convergence
         
         M1=numpy.array([[2.,1.,0.],[0.,1.,1.], [0.,0.,1.]])
         M1op = MatrixOperator(M1)
-        res1 = M1op.PowerMethod(M1op,100)
+        res1,_,_,_,convergence = M1op.PowerMethod(M1op,100, return_all=True)
         numpy.testing.assert_almost_equal(res1,2., decimal=4) 
-            
+        numpy.testing.assert_equal(convergence,True)     
 
         # Gradient Operator (float)
         ig = ImageGeometry(30,30)