diff --git a/qutip/core/environment.py b/qutip/core/environment.py
index fe10c838e0..17a1b6dce0 100644
--- a/qutip/core/environment.py
+++ b/qutip/core/environment.py
@@ -574,7 +574,7 @@ def approx_by_sd_fit(
         self, wlist: ArrayLike, Nk: int = 1, target_rsme: float = 5e-6,
         Nmax: int = 10, guess: list[float] = None, lower: list[float] = None,
         upper: list[float] = None, tag: Any = None, combine: bool = True,
-        sigma: float = 1e-4, maxfev: int = 1e-6
+        sigma: float = 1e-4, maxfev: int = 100_000
     ) -> tuple[ExponentialBosonicEnvironment, dict[str, Any]]:
         r"""
         Generates an approximation to this environment by fitting its spectral
diff --git a/qutip/tests/core/test_environment.py b/qutip/tests/core/test_environment.py
index dff626face..cb59190175 100644
--- a/qutip/tests/core/test_environment.py
+++ b/qutip/tests/core/test_environment.py
@@ -123,7 +123,7 @@ def test_approx_by_cf_fit(self, params):
             bb5 = BosonicEnvironment.from_correlation_function(
                 corr[k], t, T=T[k])
             bb6, finfo = bb5.approx_by_cf_fit(
-                t, target_rsme=None, Nr_max=2, Ni_max=1)
+                t, target_rsme=None, Nr_max=2, Ni_max=1,sigma=1e-2)
             assert np.isclose(bb6.correlation_function(t),
                               corr[k], atol=5*comtol).all()
             assert np.isclose(bb6.power_spectrum(w2), power(
@@ -136,7 +136,7 @@ def test_approx_by_sd_fit(self, params):
         for k in range(len(lam)):
             sd = spectral_density(t, gamma[k], w0[k], lam[k])
             bb5 = BosonicEnvironment.from_spectral_density(sd, t, T=T[k])
-            bb6, finfo = bb5.approx_by_sd_fit(w, Nmax=1, Nk=10)
+            bb6, finfo = bb5.approx_by_sd_fit(w, Nmax=1, Nk=10,sigma=1)
             # asking for more precision that the Bosonic enviroment has may
             # violate this (due to the interpolation and it's easily fixed
             # using a denser range). I could have set N=1 but thought this was