diff --git a/jax_galsim/moffat.py b/jax_galsim/moffat.py
index 23e5588a..22d4e16e 100644
--- a/jax_galsim/moffat.py
+++ b/jax_galsim/moffat.py
@@ -29,10 +29,12 @@ def _Knu(nu, x):
 @implements(
     _galsim.Moffat,
     lax_description="""\
-The LAX version of the Moffat profile
+The JAX-GalSim version of the Moffat profile
 
 - does not support truncation or beta < 1.1
 - does not support gsparams.maxk_thresholds > 0.1
+- does not support autodiff with respect to the `beta` parameter
+  for Fourier-space evaluations
 """,
 )
 @register_pytree_node_class
@@ -333,8 +335,10 @@ def _kValue_untrunc_interp_coeffs(self):
         k_min = 0
         k_max = self._maxk
         k = jnp.linspace(k_min, k_max, n_pts)
+
+        beta = jax.lax.stop_gradient(self.beta)
         vals = self._kValue_untrunc_func(
-            self.beta,
+            beta,
             k,
             self._knorm_bis,
             self._knorm,
@@ -343,9 +347,7 @@ def _kValue_untrunc_interp_coeffs(self):
 
         # slope to match the interpolant onto an asymptotic expansion of kv
         # that is kv(x) ~ sqrt(pi/2/x) * exp(-x) * (1 + slp/x)
-        aval = self._kValue_untrunc_asymp_func(
-            self.beta, k[-1], self._knorm_bis, self._r0
-        )
+        aval = self._kValue_untrunc_asymp_func(beta, k[-1], self._knorm_bis, self._r0)
         slp = (vals[-1] / aval - 1) * k[-1] * self._r0
 
         return k, vals, akima_interp_coeffs(k, vals), slp
@@ -355,6 +357,9 @@ def _kValue(self, kpos):
         """computation of the Moffat response in k-space with interpolant + expansions
         kpos can be a scalar or a vector (typically, scalar for debug and 2D considering an image)
         """
+        # we cannot compute gradients with respect to beta
+        beta = jax.lax.stop_gradient(self.beta)
+
         k = safe_sqrt(kpos.x**2 + kpos.y**2)
         out_shape = jnp.shape(k)
         k = jnp.atleast_1d(k)
@@ -364,7 +369,12 @@ def _kValue(self, kpos):
         k_msk = jnp.where(k > 0, k, k_[1])
         res = jnp.where(
             k > k_[-1],
-            self._kValue_untrunc_asymp_func(self.beta, k_msk, self._knorm_bis, self._r0)
+            self._kValue_untrunc_asymp_func(
+                beta,
+                k_msk,
+                self._knorm_bis,
+                self._r0,
+            )
             * (1.0 + slp / k_msk / self._r0),
             res,
         )
diff --git a/jax_galsim/spergel.py b/jax_galsim/spergel.py
index b0bf22a8..9ffd9e86 100644
--- a/jax_galsim/spergel.py
+++ b/jax_galsim/spergel.py
@@ -254,7 +254,10 @@ def _spergel_hlr_pade(x):
 
             \hat{I}(k) = flux / (1 + (k r_0)^2)^{1+\nu}
 
-    where :math:`r_0` is the ``scale_radius``, and :math: `\nu` mandatory to be in [-0.85,4.0]
+    where :math:`r_0` is the ``scale_radius``, and :math:`\nu` mandatory to be in [-0.85,4.0]
+
+    The JAX-GalSim implementation does not support autodiff with respect to :math:`\nu` for
+    real-space evaluations.
     """,
 )
 @register_pytree_node_class
@@ -411,7 +414,7 @@ def _max_sb(self):
     @jax.jit
     def _xValue(self, pos):
         r = jnp.sqrt(pos.x**2 + pos.y**2) * self._inv_r0
-        res = jnp.where(r == 0, self._xnorm0, fz_nu(r, self.nu))
+        res = jnp.where(r == 0, self._xnorm0, fz_nu(r, jax.lax.stop_gradient(self.nu)))
         return self._xnorm * res
 
     @jax.jit
diff --git a/tests/jax/test_deriv_gsobject.py b/tests/jax/test_deriv_gsobject.py
index 73dbd22e..1c24beb9 100644
--- a/tests/jax/test_deriv_gsobject.py
+++ b/tests/jax/test_deriv_gsobject.py
@@ -31,7 +31,7 @@ def _run(val_):
                     **kwargs_,
                     gsparams=jgs.GSParams(minimum_fft_size=8, maximum_fft_size=8),
                 )
-                .drawImage(nx=5, ny=5, scale=0.2, method="fft")
+                .drawImage(nx=5, ny=5, scale=0.2)
                 .array[2, 2]
                 ** 2
             )
@@ -44,3 +44,29 @@ def _run(val_):
         atol = 1e-5
 
         np.testing.assert_allclose(gval, gfdiff, rtol=0, atol=atol)
+
+
+def test_deriv_gsobject_spergel_nu():
+    val = 2.0
+    eps = 1e-5
+
+    def _run(val_):
+        return jnp.max(
+            jgs.Spergel(
+                val,
+                scale_radius=2.0,
+                gsparams=jgs.GSParams(minimum_fft_size=8, maximum_fft_size=8),
+            )
+            .drawImage(nx=5, ny=5, scale=0.2)
+            .array[2, 2]
+            ** 2
+        )
+
+    gfunc = jax.jit(jax.grad(_run))
+    gval = gfunc(val)
+
+    gfdiff = (_run(val + eps) - _run(val - eps)) / 2.0 / eps
+
+    atol = 1e-5
+
+    np.testing.assert_allclose(gval, gfdiff, rtol=0, atol=atol)