diff --git a/mesmer/stats/_harmonic_model.py b/mesmer/stats/_harmonic_model.py
index 14cc544c..39be2cb3 100644
--- a/mesmer/stats/_harmonic_model.py
+++ b/mesmer/stats/_harmonic_model.py
@@ -143,11 +143,12 @@ def residuals_from_fourier_series(coeffs, yearly_predictor, mon_target):
         residuals_from_fourier_series,
         first_guess,
         args=(yearly_predictor, monthly_target),
+        loss="linear",
         method="lm",
     )
 
     coeffs = minimize_result.x
-    mse = np.mean(minimize_result.func**2)
+    mse = np.mean(minimize_result.fun**2)
 
     return coeffs, mse
 
diff --git a/mesmer/stats/_power_transformer.py b/mesmer/stats/_power_transformer.py
index f0ef73c9..e21b24b2 100644
--- a/mesmer/stats/_power_transformer.py
+++ b/mesmer/stats/_power_transformer.py
@@ -177,10 +177,7 @@ def _neg_log_likelihood(coeffs):
     first_guess = np.array([1, 0])
 
     xi_0, xi_1 = minimize(
-        _neg_log_likelihood,
-        x0=first_guess,
-        bounds=bounds,
-        method="Nelder-Mead",
+        _neg_log_likelihood, x0=first_guess, bounds=bounds, method="L-BFGS-B", jac="cs"
     ).x
 
     return xi_0, xi_1
diff --git a/tests/integration/test_calibrate_mesmer_m.py b/tests/integration/test_calibrate_mesmer_m.py
index 3a595bb0..38a40570 100644
--- a/tests/integration/test_calibrate_mesmer_m.py
+++ b/tests/integration/test_calibrate_mesmer_m.py
@@ -1,6 +1,5 @@
 import importlib
 
-import numpy as np
 import pytest
 import xarray as xr
 
@@ -72,22 +71,22 @@ def mask_and_stack(ds, threshold_land):
     m_time = tas_stacked_m.time
 
     # fit harmonic model
-    # harmonic_model_fit = mesmer.stats.fit_harmonic_model(
-    #     tas_stacked_y.tas, tas_stacked_m.tas
-    # )
-    expected_params = xr.open_dataset(
-        TEST_PATH / "test-mesmer_m-params.nc", use_cftime=True
-    )
-    hm_preds = mesmer.stats.predict_harmonic_model(
-        tas_stacked_y.tas, expected_params.hm_coeffs, expected_params.monthly_time
-    )
-    harmonic_model_fit = xr.merge(
-        [
-            expected_params.hm_coeffs.rename("coeffs"),
-            expected_params.hm_nsel.rename("n_sel"),
-            hm_preds.rename("predictions"),
-        ]
+    harmonic_model_fit = mesmer.stats.fit_harmonic_model(
+        tas_stacked_y.tas, tas_stacked_m.tas
     )
+    # expected_params = xr.open_dataset(
+    #     TEST_PATH / "test-mesmer_m-params.nc", use_cftime=True
+    # )
+    # hm_preds = mesmer.stats.predict_harmonic_model(
+    #     tas_stacked_y.tas, expected_params.hm_coeffs, expected_params.monthly_time
+    # )
+    # harmonic_model_fit = xr.merge(
+    #     [
+    #         expected_params.hm_coeffs.rename("coeffs"),
+    #         expected_params.hm_nsel.rename("n_sel"),
+    #         hm_preds.rename("predictions"),
+    #     ]
+    # )
 
     # train power transformer
     resids_after_hm = tas_stacked_m - harmonic_model_fit.predictions
@@ -142,7 +141,7 @@ def mask_and_stack(ds, threshold_land):
             TEST_PATH / "test-mesmer_m-params.nc", use_cftime=True
         )
         # np.testing.assert_allclose(expected_params.hm_coeffs.values, calibrated_params.hm_coeffs.values, atol=1e-7)
-        np.testing.assert_allclose(
-            expected_params.pt_xi0.values, calibrated_params.pt_xi0.values
-        )
-        xr.testing.assert_allclose(expected_params, calibrated_params)
+        # np.testing.assert_allclose(
+        #     expected_params.pt_xi0.values, calibrated_params.pt_xi0.values
+        # )
+        xr.testing.assert_allclose(expected_params, calibrated_params, atol=1e-4)
diff --git a/tests/test-data/output/tas/mon/test-mesmer_m-params.nc b/tests/test-data/output/tas/mon/test-mesmer_m-params.nc
index a060407d..1620a5de 100644
Binary files a/tests/test-data/output/tas/mon/test-mesmer_m-params.nc and b/tests/test-data/output/tas/mon/test-mesmer_m-params.nc differ