diff --git a/test/test_operators/test_adjoint.py b/test/test_operators/test_adjoint.py
index 0a0c4b278e789d4ee3a39f686ac469468e1b4196..124588bd5dc48ebe4406baaeba7763a345c93110 100644
--- a/test/test_operators/test_adjoint.py
+++ b/test/test_operators/test_adjoint.py
@@ -9,8 +9,17 @@ from numpy.testing import assert_allclose
 def _check_adjointness(op, dtype=np.float64):
     f1 = ift.Field.from_random("normal", domain=op.domain, dtype=dtype)
     f2 = ift.Field.from_random("normal", domain=op.target, dtype=dtype)
-    assert_allclose(f1.vdot(op.adjoint_times(f2)), op.times(f1).vdot(f2),
-                    rtol=1e-8)
+    cap = op.capability
+    if ((cap & ift.LinearOperator.TIMES) and
+            (cap & ift.LinearOperator.ADJOINT_TIMES)):
+        assert_allclose(f1.vdot(op.adjoint_times(f2)),
+                        op.times(f1).vdot(f2),
+                        rtol=1e-8)
+    if ((cap & ift.LinearOperator.INVERSE_TIMES) and
+            (cap & ift.LinearOperator.INVERSE_ADJOINT_TIMES)):
+        assert_allclose(f1.vdot(op.inverse_times(f2)),
+                        op.inverse_adjoint_times(f1).vdot(f2),
+                        rtol=1e-8)
 
 _harmonic_spaces = [ift.RGSpace(7, distances=0.2, harmonic=True),
                     ift.RGSpace((12, 46), distances=(0.2, 0.3), harmonic=True),
@@ -41,3 +50,5 @@ class Adjointness_Tests(unittest.TestCase):
     def testFFT(self, sp, dtype):
         op = ift.FFTOperator(sp)
         _check_adjointness(op, dtype)
+        op = ift.FFTOperator(sp.get_default_codomain())
+        _check_adjointness(op, dtype)
diff --git a/test/test_operators/test_fft_operator.py b/test/test_operators/test_fft_operator.py
index 63ba59cb6e5d80cb7ecb33f0e8377685e0f9a918..95052965ea0235242d3dd6c544d69c682ea55ce6 100644
--- a/test/test_operators/test_fft_operator.py
+++ b/test/test_operators/test_fft_operator.py
@@ -39,9 +39,18 @@ class FFTOperatorTests(unittest.TestCase):
         tol = _get_rtol(itp)
         a = ift.RGSpace(dim1, distances=d)
         b = ift.RGSpace(dim1, distances=1./(dim1*d), harmonic=True)
+        np.random.seed(16)
+
         fft = ift.FFTOperator(domain=a, target=b)
+        inp = ift.Field.from_random(domain=a, random_type='normal',
+                                    std=7, mean=3, dtype=itp)
+        out = fft.inverse_times(fft.times(inp))
+        assert_allclose(ift.dobj.to_global_data(inp.val),
+                        ift.dobj.to_global_data(out.val), rtol=tol, atol=tol)
 
-        np.random.seed(16)
+        a, b = b, a
+
+        fft = ift.FFTOperator(domain=a, target=b)
         inp = ift.Field.from_random(domain=a, random_type='normal',
                                     std=7, mean=3, dtype=itp)
         out = fft.inverse_times(fft.times(inp))
@@ -56,8 +65,18 @@ class FFTOperatorTests(unittest.TestCase):
         a = ift.RGSpace([dim1, dim2], distances=[d1, d2])
         b = ift.RGSpace([dim1, dim2],
                         distances=[1./(dim1*d1), 1./(dim2*d2)], harmonic=True)
+
+        fft = ift.FFTOperator(domain=a, target=b)
+        inp = ift.Field.from_random(domain=a, random_type='normal',
+                                    std=7, mean=3, dtype=itp)
+        out = fft.inverse_times(fft.times(inp))
+        assert_allclose(ift.dobj.to_global_data(inp.val),
+                        ift.dobj.to_global_data(out.val), rtol=tol, atol=tol)
         fft = ift.FFTOperator(domain=a, target=b)
 
+        a, b = b, a
+
+        fft = ift.FFTOperator(domain=a, target=b)
         inp = ift.Field.from_random(domain=a, random_type='normal',
                                     std=7, mean=3, dtype=itp)
         out = fft.inverse_times(fft.times(inp))
@@ -132,6 +151,7 @@ class FFTOperatorTests(unittest.TestCase):
         assert_allclose(v1, v2, rtol=tol, atol=tol)
 
     @expand(product([ift.RGSpace(128, distances=3.76, harmonic=True),
+                     ift.RGSpace(73, distances=0.5643),
                      ift.LMSpace(lmax=30, mmax=25)],
                     [np.float64, np.float32, np.complex64, np.complex128]))
     def test_normalisation(self, space, tp):