diff --git a/demos/Wiener_Filter.ipynb b/demos/Wiener_Filter.ipynb
index 1754210855c62bbedd755e0db45f734f626cab0e..b0ef1f8b38a3e372d0c120a45bceaabe287e35c0 100644
--- a/demos/Wiener_Filter.ipynb
+++ b/demos/Wiener_Filter.ipynb
@@ -240,7 +240,7 @@
     "sh = Sh.draw_sample()\n",
     "noiseless_data=R(sh)\n",
     "noise_amplitude = np.sqrt(0.2)\n",
-    "N = ift.ScalingOperator(noise_amplitude**2, s_space)\n",
+    "N = ift.ScalingOperator(s_space, noise_amplitude**2)\n",
     "\n",
     "n = ift.Field.from_random(domain=s_space, random_type='normal',\n",
     "                          std=noise_amplitude, mean=0)\n",
@@ -391,7 +391,7 @@
    "source": [
     "# Operators\n",
     "Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)\n",
-    "N = ift.ScalingOperator(noise_amplitude**2,s_space)\n",
+    "N = ift.ScalingOperator(s_space, noise_amplitude**2)\n",
     "# R is defined below\n",
     "\n",
     "# Fields\n",
@@ -569,7 +569,7 @@
     "\n",
     "# Operators\n",
     "Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)\n",
-    "N = ift.ScalingOperator(sigma2,s_space)\n",
+    "N = ift.ScalingOperator(s_space, sigma2)\n",
     "\n",
     "# Fields and data\n",
     "sh = Sh.draw_sample()\n",
diff --git a/demos/getting_started_1.py b/demos/getting_started_1.py
index 3698549a02ba2640b895fdf6019824a90c8f7537..886a4ceaa7362f7ae73d90a92221536e45e359d1 100644
--- a/demos/getting_started_1.py
+++ b/demos/getting_started_1.py
@@ -113,7 +113,7 @@ if __name__ == '__main__':
 
     # Set the noise covariance N
     noise = 5.
-    N = ift.ScalingOperator(noise, data_space)
+    N = ift.ScalingOperator(data_space, noise)
 
     # Create mock data
     MOCK_SIGNAL = S.draw_sample()
diff --git a/demos/getting_started_3.py b/demos/getting_started_3.py
index 2032c6b8c1dc442d53df0cdecbdcfaaf24836e09..c3fdbb83b0206ec923f29366879399bc1910ccbd 100644
--- a/demos/getting_started_3.py
+++ b/demos/getting_started_3.py
@@ -74,7 +74,7 @@ if __name__ == '__main__':
     # Specify noise
     data_space = R.target
     noise = .001
-    N = ift.ScalingOperator(noise, data_space)
+    N = ift.ScalingOperator(data_space, noise)
 
     # Generate mock signal and data
     mock_position = ift.from_random('normal', signal_response.domain)
diff --git a/demos/getting_started_mf.py b/demos/getting_started_mf.py
index d02ba63c73d9f0ff13dd31dfc1d01054435f9fb8..1883f9a13433528f7055b64e736b06c55819dacb 100644
--- a/demos/getting_started_mf.py
+++ b/demos/getting_started_mf.py
@@ -93,7 +93,7 @@ if __name__ == '__main__':
     # Specify noise
     data_space = R.target
     noise = .001
-    N = ift.ScalingOperator(noise, data_space)
+    N = ift.ScalingOperator(data_space, noise)
 
     # Generate mock signal and data
     mock_position = ift.from_random('normal', signal_response.domain)
diff --git a/nifty6/library/adjust_variances.py b/nifty6/library/adjust_variances.py
index e83c693f6a9ab21a5aefaa37358f232d6a84be61..1f3c624e897ae6312383a0e6f4be3b1b842cca57 100644
--- a/nifty6/library/adjust_variances.py
+++ b/nifty6/library/adjust_variances.py
@@ -72,7 +72,7 @@ def make_adjust_variances_hamiltonian(a,
 
     x = (a.conjugate()*a).real
     if scaling is not None:
-        x = ScalingOperator(scaling, x.target)(x)
+        x = ScalingOperator(x.target, scaling)(x)
 
     return StandardHamiltonian(InverseGammaLikelihood(d_eval/2.)(x),
                                ic_samp=ic_samp)
diff --git a/nifty6/library/dynamic_operator.py b/nifty6/library/dynamic_operator.py
index 8a16ae3eae9ff4b038463a6d0a7184bd1a57a95c..32f991141acba990ae1fb2392eecd3ec89e1c803 100644
--- a/nifty6/library/dynamic_operator.py
+++ b/nifty6/library/dynamic_operator.py
@@ -74,7 +74,7 @@ def _make_dynamic_operator(target,
     ops['FFT'] = FFT
     ops['Real'] = Real
     if harmonic_padding is None:
-        CentralPadd = ScalingOperator(1., FFT.target)
+        CentralPadd = ScalingOperator(FFT.target, 1.)
     else:
         if isinstance(harmonic_padding, int):
             harmonic_padding = list((harmonic_padding,)*len(FFT.target.shape))
@@ -123,7 +123,7 @@ def _make_dynamic_operator(target,
         c = FieldAdapter(UnstructuredDomain(len(sigc)), keys[1])
         c = makeOp(Field(c.target, np.array(sigc)))(c)
 
-        lightspeed = ScalingOperator(-0.5, c.target)(c).exp()
+        lightspeed = ScalingOperator(c.target, -0.5)(c).exp()
         scaling = np.array(m.target[0].distances[1:])/m.target[0].distances[0]
         scaling = DiagonalOperator(Field(c.target, scaling))
         ops['lightspeed'] = scaling(lightspeed)
diff --git a/nifty6/linearization.py b/nifty6/linearization.py
index d62d5b402fb7731874c73cbc5966011192ef25a2..8b1787056eea1b040b5e661f370aaf5fc235bbe7 100644
--- a/nifty6/linearization.py
+++ b/nifty6/linearization.py
@@ -406,7 +406,7 @@ class Linearization(object):
             the requested Linearization
         """
         from .operators.scaling_operator import ScalingOperator
-        return Linearization(field, ScalingOperator(1., field.domain),
+        return Linearization(field, ScalingOperator(field.domain, 1.),
                              want_metric=want_metric)
 
     @staticmethod
@@ -492,7 +492,7 @@ class Linearization(object):
         if len(constants) == 0:
             return Linearization.make_var(field, want_metric)
         else:
-            ops = {key: ScalingOperator(0. if key in constants else 1., dom)
+            ops = {key: ScalingOperator(dom, 0. if key in constants else 1.)
                    for key, dom in field.domain.items()}
             bdop = BlockDiagonalOperator(field.domain, ops)
             return Linearization(field, bdop, want_metric=want_metric)
diff --git a/nifty6/operators/chain_operator.py b/nifty6/operators/chain_operator.py
index af46f4fefe5d1914745fd8164bbdb6549b05ed2a..78d83ef820595e1ac49b5a0dd30b8c07c1be21a0 100644
--- a/nifty6/operators/chain_operator.py
+++ b/nifty6/operators/chain_operator.py
@@ -72,7 +72,7 @@ class ChainOperator(LinearOperator):
                     break
         if fct != 1 or len(opsnew) == 0:
             # have to add the scaling operator at the end
-            opsnew.append(ScalingOperator(fct, lastdom))
+            opsnew.append(ScalingOperator(lastdom, fct))
         ops = opsnew
         # combine DiagonalOperators where possible
         opsnew = []
diff --git a/nifty6/operators/energy_operators.py b/nifty6/operators/energy_operators.py
index 221d70e4bbd062aa043684c14303978746731844..b748a1fccb142a4e9a55fef5063e596cda855568 100644
--- a/nifty6/operators/energy_operators.py
+++ b/nifty6/operators/energy_operators.py
@@ -276,7 +276,7 @@ class StudentTEnergy(EnergyOperator):
             return Field.scalar(v)
         if not x.want_metric:
             return v
-        met = ScalingOperator((self._theta+1)/(self._theta+3), self.domain)
+        met = ScalingOperator(self.domain, (self._theta+1) / (self._theta+3))
         met = SandwichOperator.make(x.jac, met)
         return v.add_metric(met)
 
diff --git a/nifty6/operators/harmonic_operators.py b/nifty6/operators/harmonic_operators.py
index bd4a5e33739e173e34be6d55486d186faf9490d1..76b6f1157378a3a3546a9dcf39c645c20bf5458e 100644
--- a/nifty6/operators/harmonic_operators.py
+++ b/nifty6/operators/harmonic_operators.py
@@ -345,7 +345,7 @@ def HarmonicSmoothingOperator(domain, sigma, space=None):
     if sigma < 0.:
         raise ValueError("sigma must be non-negative")
     if sigma == 0.:
-        return ScalingOperator(1., domain)
+        return ScalingOperator(domain, 1.)
 
     domain = DomainTuple.make(domain)
     space = utilities.infer_space(domain, space)
diff --git a/nifty6/operators/operator.py b/nifty6/operators/operator.py
index 4790da315d6925a39c2b60643e1005d035419cd0..4d2ebcc51d4e851ecf0f23ca230fda50d967d445 100644
--- a/nifty6/operators/operator.py
+++ b/nifty6/operators/operator.py
@@ -60,7 +60,7 @@ class Operator(metaclass=NiftyMeta):
         if factor == 1:
             return self
         from .scaling_operator import ScalingOperator
-        return ScalingOperator(factor, self.target)(self)
+        return ScalingOperator(self.target, factor)(self)
 
     def conjugate(self):
         from .simple_linear_operators import ConjugationOperator
diff --git a/nifty6/operators/sandwich_operator.py b/nifty6/operators/sandwich_operator.py
index cfc4333efd92686976148838f8c0a06d20315d9f..07a451261dac4f85e666e69aeb6c25bf06c603bc 100644
--- a/nifty6/operators/sandwich_operator.py
+++ b/nifty6/operators/sandwich_operator.py
@@ -57,7 +57,7 @@ class SandwichOperator(EndomorphicOperator):
         if cheese is not None and not isinstance(cheese, LinearOperator):
             raise TypeError("cheese must be a linear operator or None")
         if cheese is None:
-            cheese = ScalingOperator(1., bun.target)
+            cheese = ScalingOperator(bun.target, 1.)
             op = bun.adjoint(bun)
         else:
             op = bun.adjoint(cheese(bun))
diff --git a/nifty6/operators/scaling_operator.py b/nifty6/operators/scaling_operator.py
index 688b338a0b5776ff0eac4d99885d910fde27fff8..81e4ffb062a10ea76198d358162063460490eeaa 100644
--- a/nifty6/operators/scaling_operator.py
+++ b/nifty6/operators/scaling_operator.py
@@ -26,10 +26,10 @@ class ScalingOperator(EndomorphicOperator):
 
     Parameters
     ----------
-    factor : scalar
-        The multiplication factor
     domain : Domain or tuple of Domain or DomainTuple
         The domain on which the Operator's input Field is defined.
+    factor : scalar
+        The multiplication factor
 
     Notes
     -----
@@ -50,13 +50,13 @@ class ScalingOperator(EndomorphicOperator):
     somewhere else.
     """
 
-    def __init__(self, factor, domain):
+    def __init__(self, domain, factor):
         from ..sugar import makeDomain
 
         if not np.isscalar(factor):
             raise TypeError("Scalar required")
-        self._factor = factor
         self._domain = makeDomain(domain)
+        self._factor = factor
         self._capability = self._all_ops
 
     def apply(self, x, mode):
@@ -81,7 +81,7 @@ class ScalingOperator(EndomorphicOperator):
             fct = np.conj(fct)
         if trafo & self.INVERSE_BIT:
             fct = 1./fct
-        return ScalingOperator(fct, self._domain)
+        return ScalingOperator(self._domain, fct)
 
     def _get_fct(self, from_inverse):
         fct = self._factor
diff --git a/nifty6/operators/sum_operator.py b/nifty6/operators/sum_operator.py
index ca8a76847a41883ab86f72e2f14b3422eef4bdb4..d2b06be7c3e563598a605e07636553dfd0c83580 100644
--- a/nifty6/operators/sum_operator.py
+++ b/nifty6/operators/sum_operator.py
@@ -99,7 +99,7 @@ class SumOperator(LinearOperator):
                         break
             if sum != 0 or len(opsnew) == 0:
                 # have to add the scaling operator at the end
-                opsnew.append(ScalingOperator(sum, lastdom))
+                opsnew.append(ScalingOperator(lastdom, sum))
                 negnew.append(False)
 
             ops = opsnew
diff --git a/nifty6/sugar.py b/nifty6/sugar.py
index 6341bbc47943376bdca2eaee9e05731d9e8c98e9..7b0318246e35629706cd052108b3db2a72ee9975 100644
--- a/nifty6/sugar.py
+++ b/nifty6/sugar.py
@@ -493,7 +493,7 @@ def calculate_position(operator, output):
     if output.domain != operator.target:
         raise TypeError
     cov = 1e-3*output.val.max()**2
-    invcov = ScalingOperator(cov, output.domain).inverse
+    invcov = ScalingOperator(output.domain, cov).inverse
     d = output + invcov.draw_sample(from_inverse=True)
     lh = GaussianEnergy(d, invcov)(operator)
     H = StandardHamiltonian(
diff --git a/test/test_energy_gradients.py b/test/test_energy_gradients.py
index 9797ad8d91a268c2f5fb31666525d4b4b2c6f711..6d295d9d46356bb67d242931b9b89ef435a1d4bd 100644
--- a/test/test_energy_gradients.py
+++ b/test/test_energy_gradients.py
@@ -37,7 +37,7 @@ PARAMS = product(SEEDS, SPACES)
 @pytest.fixture(params=PARAMS)
 def field(request):
     np.random.seed(request.param[0])
-    S = ift.ScalingOperator(1., request.param[1])
+    S = ift.ScalingOperator(request.param[1], 1.)
     s = S.draw_sample()
     return ift.MultiField.from_dict({'s1': s})['s1']
 
@@ -76,7 +76,7 @@ def test_hamiltonian_and_KL(field):
     lh = ift.GaussianEnergy(domain=space)
     hamiltonian = ift.StandardHamiltonian(lh)
     ift.extra.check_jacobian_consistency(hamiltonian, field)
-    S = ift.ScalingOperator(1., space)
+    S = ift.ScalingOperator(space, 1.)
     samps = [S.draw_sample() for i in range(3)]
     kl = ift.AveragedEnergy(hamiltonian, samps)
     ift.extra.check_jacobian_consistency(kl, field)
diff --git a/test/test_gaussian_energy.py b/test/test_gaussian_energy.py
index c802187ebd5aeea5d0a715ee6b8e4410432ef147..e317aac151c864fb6985baec2ddf9a511e431ef4 100644
--- a/test/test_gaussian_energy.py
+++ b/test/test_gaussian_energy.py
@@ -51,9 +51,9 @@ def test_gaussian_energy(space, nonlinearity, noise, seed):
 
     pspec = ift.PS_field(pspace, pspec)
     A = Dist(ift.sqrt(pspec))
-    N = ift.ScalingOperator(noise, space)
+    N = ift.ScalingOperator(space, noise)
     n = N.draw_sample()
-    R = ift.ScalingOperator(10., space)
+    R = ift.ScalingOperator(space, 10.)
 
     def d_model():
         if nonlinearity == "":
diff --git a/test/test_multi_field.py b/test/test_multi_field.py
index e29fd31873b1d03fcd83e60a195d3dce7d44c946..5d06f6fd5316e9e61412285695165f0457e5bc6a 100644
--- a/test/test_multi_field.py
+++ b/test/test_multi_field.py
@@ -58,7 +58,7 @@ def test_dataconv():
 
 def test_blockdiagonal():
     op = ift.BlockDiagonalOperator(
-        dom, {"d1": ift.ScalingOperator(20., dom["d1"])})
+        dom, {"d1": ift.ScalingOperator(dom["d1"], 20.)})
     op2 = op(op)
     ift.extra.consistency_check(op2)
     assert_equal(type(op2), ift.BlockDiagonalOperator)
diff --git a/test/test_operators/test_composed_operator.py b/test/test_operators/test_composed_operator.py
index cfe587dc02d44cf997076092580465bcccc75dd0..15d93db5bf4e64af58cdcad3913dbf134e6459cc 100644
--- a/test/test_operators/test_composed_operator.py
+++ b/test/test_operators/test_composed_operator.py
@@ -65,7 +65,7 @@ def test_times_inverse_times(space1, space2):
 
 def test_sum(space1):
     op1 = ift.makeOp(ift.Field.full(space1, 2.))
-    op2 = ift.ScalingOperator(3., space1)
+    op2 = ift.ScalingOperator(space1, 3.)
     full_op = op1 + op2 - (op2 - op1) + op1 + op1 + op2
     x = ift.Field.full(space1, 1.)
     res = full_op(x)
@@ -75,7 +75,7 @@ def test_sum(space1):
 
 def test_chain(space1):
     op1 = ift.makeOp(ift.Field.full(space1, 2.))
-    op2 = ift.ScalingOperator(3., space1)
+    op2 = ift.ScalingOperator(space1, 3.,)
     full_op = op1(op2)(op2)(op1)(op1)(op1)(op2)
     x = ift.Field.full(space1, 1.)
     res = full_op(x)
@@ -85,7 +85,7 @@ def test_chain(space1):
 
 def test_mix(space1):
     op1 = ift.makeOp(ift.Field.full(space1, 2.))
-    op2 = ift.ScalingOperator(3., space1)
+    op2 = ift.ScalingOperator(space1, 3.)
     full_op = op1(op2 + op2)(op1)(op1) - op1(op2)
     x = ift.Field.full(space1, 1.)
     res = full_op(x)
diff --git a/test/test_operators/test_jacobian.py b/test/test_operators/test_jacobian.py
index 48a9feb21fed88e980aa840b6cf16c4464651cb1..7228574884e4a0ac583ca2b9112d8864cd7e4dad 100644
--- a/test/test_operators/test_jacobian.py
+++ b/test/test_operators/test_jacobian.py
@@ -39,10 +39,10 @@ seed = list2fixture([4, 78, 23])
 
 def testBasics(space, seed):
     np.random.seed(seed)
-    S = ift.ScalingOperator(1., space)
+    S = ift.ScalingOperator(space, 1.)
     s = S.draw_sample()
     var = ift.Linearization.make_var(s)
-    model = ift.ScalingOperator(6., var.target)
+    model = ift.ScalingOperator(var.target, 6.)
     ift.extra.check_jacobian_consistency(model, var.val)
 
 
@@ -64,7 +64,7 @@ def testBinary(type1, type2, space, seed):
     model = select_s1.scale(3.)
     pos = ift.from_random("normal", dom1)
     ift.extra.check_jacobian_consistency(model, pos, ntries=20)
-    model = ift.ScalingOperator(2.456, space)(select_s1*select_s2)
+    model = ift.ScalingOperator(space, 2.456)(select_s1*select_s2)
     pos = ift.from_random("normal", dom)
     ift.extra.check_jacobian_consistency(model, pos, ntries=20)
     model = ift.sigmoid(2.456*(select_s1*select_s2))
@@ -90,7 +90,7 @@ def testBinary(type1, type2, space, seed):
 
 
 def testPointModel(space, seed):
-    S = ift.ScalingOperator(1., space)
+    S = ift.ScalingOperator(space, 1.)
     pos = S.draw_sample()
     alpha = 1.5
     q = 0.73
@@ -118,7 +118,7 @@ def testDynamicModel(target, causal, minimum_phase, seed):
             'minimum_phase': minimum_phase
             }
     model, _ = ift.dynamic_operator(**dct)
-    S = ift.ScalingOperator(1., model.domain)
+    S = ift.ScalingOperator(model.domain, 1.)
     pos = S.draw_sample()
     # FIXME I dont know why smaller tol fails for 3D example
     ift.extra.check_jacobian_consistency(model, pos, tol=1e-5, ntries=20)
@@ -139,7 +139,7 @@ def testDynamicModel(target, causal, minimum_phase, seed):
         dct['sigc'] = 1.
         dct['quant'] = 5
         model, _ = ift.dynamic_lightcone_operator(**dct)
-        S = ift.ScalingOperator(1., model.domain)
+        S = ift.ScalingOperator(model.domain, 1.)
         pos = S.draw_sample()
         # FIXME I dont know why smaller tol fails for 3D example
         ift.extra.check_jacobian_consistency(