diff --git a/tests/integration/test_optimisation_options.py b/tests/integration/test_optimisation_options.py
index 796090c4..f88720ea 100644
--- a/tests/integration/test_optimisation_options.py
+++ b/tests/integration/test_optimisation_options.py
@@ -56,7 +56,7 @@ def noise(self, sigma, values):
     def spm_costs(self, model, parameters, cost_class):
         # Form dataset
         init_soc = 0.5
-        solution = self.getdata(model, self.ground_truth, init_soc)
+        solution = self.get_data(model, parameters, self.ground_truth, init_soc)
         dataset = pybop.Dataset(
             {
                 "Time [s]": solution["Time [s]"].data,
@@ -99,15 +99,10 @@ def test_optimisation_f_guessed(self, f_guessed, spm_costs):
 
         # Assertions
         assert initial_cost > final_cost
-        np.testing.assert_allclose(x, self.ground_truth, atol=2.5e-2)
+        np.testing.assert_allclose(x, self.ground_truth, atol=1e-2)
 
-    def getdata(self, model, x, init_soc):
-        model.parameter_set.update(
-            {
-                "Negative electrode active material volume fraction": x[0],
-                "Positive electrode active material volume fraction": x[1],
-            }
-        )
+    def get_data(self, model, parameters, x, init_soc):
+        model.parameters = parameters
         experiment = pybop.Experiment(
             [
                 (
@@ -117,5 +112,5 @@ def getdata(self, model, x, init_soc):
             ]
             * 2
         )
-        sim = model.predict(init_soc=init_soc, experiment=experiment)
+        sim = model.predict(init_soc=init_soc, experiment=experiment, inputs=x)
         return sim
diff --git a/tests/integration/test_spm_parameterisations.py b/tests/integration/test_spm_parameterisations.py
index 89ecc32f..40b4f40e 100644
--- a/tests/integration/test_spm_parameterisations.py
+++ b/tests/integration/test_spm_parameterisations.py
@@ -1,6 +1,5 @@
 import numpy as np
 import pytest
-from pybamm import __version__ as pybamm_version
 
 import pybop
 
@@ -59,7 +58,7 @@ def noise(self, sigma, values):
     @pytest.fixture
     def spm_costs(self, model, parameters, cost_class, init_soc):
         # Form dataset
-        solution = self.getdata(model, self.ground_truth, init_soc)
+        solution = self.get_data(model, parameters, self.ground_truth, init_soc)
         dataset = pybop.Dataset(
             {
                 "Time [s]": solution["Time [s]"].data,
@@ -119,16 +118,13 @@ def test_spm_optimisers(self, optimiser, spm_costs):
         # Assertions
         if not np.allclose(x0, self.ground_truth, atol=1e-5):
             assert initial_cost > final_cost
-        if pybamm_version <= "23.9":
-            np.testing.assert_allclose(x, self.ground_truth, atol=2.5e-2)
-        else:
-            np.testing.assert_allclose(x, self.ground_truth, atol=1.75e-2)
+        np.testing.assert_allclose(x, self.ground_truth, atol=1e-2)
 
     @pytest.fixture
     def spm_two_signal_cost(self, parameters, model, cost_class):
         # Form dataset
         init_soc = 0.5
-        solution = self.getdata(model, self.ground_truth, init_soc)
+        solution = self.get_data(model, parameters, self.ground_truth, init_soc)
         dataset = pybop.Dataset(
             {
                 "Time [s]": solution["Time [s]"].data,
@@ -188,7 +184,7 @@ def test_multiple_signals(self, multi_optimiser, spm_two_signal_cost):
         # Assertions
         if not np.allclose(x0, self.ground_truth, atol=1e-5):
             assert initial_cost > final_cost
-        np.testing.assert_allclose(x, self.ground_truth, atol=2.5e-2)
+        np.testing.assert_allclose(x, self.ground_truth, atol=1e-2)
 
     @pytest.mark.parametrize("init_soc", [0.4, 0.6])
     @pytest.mark.integration
@@ -199,7 +195,7 @@ def test_model_misparameterisation(self, parameters, model, init_soc):
         second_model = pybop.lithium_ion.SPMe(parameter_set=second_parameter_set)
 
         # Form dataset
-        solution = self.getdata(second_model, self.ground_truth, init_soc)
+        solution = self.get_data(second_model, parameters, self.ground_truth, init_soc)
         dataset = pybop.Dataset(
             {
                 "Time [s]": solution["Time [s]"].data,
@@ -226,13 +222,8 @@ def test_model_misparameterisation(self, parameters, model, init_soc):
             np.testing.assert_allclose(final_cost, 0, atol=1e-2)
             np.testing.assert_allclose(x, self.ground_truth, atol=2e-2)
 
-    def getdata(self, model, x, init_soc):
-        model.parameter_set.update(
-            {
-                "Negative electrode active material volume fraction": x[0],
-                "Positive electrode active material volume fraction": x[1],
-            }
-        )
+    def get_data(self, model, parameters, x, init_soc):
+        model.parameters = parameters
         experiment = pybop.Experiment(
             [
                 (
@@ -242,5 +233,5 @@ def getdata(self, model, x, init_soc):
             ]
             * 2
         )
-        sim = model.predict(init_soc=init_soc, experiment=experiment)
+        sim = model.predict(init_soc=init_soc, experiment=experiment, inputs=x)
         return sim
diff --git a/tests/integration/test_thevenin_parameterisation.py b/tests/integration/test_thevenin_parameterisation.py
index ed0ff154..cc2a52c6 100644
--- a/tests/integration/test_thevenin_parameterisation.py
+++ b/tests/integration/test_thevenin_parameterisation.py
@@ -49,7 +49,7 @@ def cost_class(self, request):
     @pytest.fixture
     def cost(self, model, parameters, cost_class):
         # Form dataset
-        solution = self.getdata(model, self.ground_truth)
+        solution = self.get_data(model, parameters, self.ground_truth)
         dataset = pybop.Dataset(
             {
                 "Time [s]": solution["Time [s]"].data,
@@ -88,13 +88,8 @@ def test_optimisers_on_simple_model(self, optimiser, cost):
             assert initial_cost > final_cost
         np.testing.assert_allclose(x, self.ground_truth, atol=1e-2)
 
-    def getdata(self, model, x):
-        model.parameter_set.update(
-            {
-                "R0 [Ohm]": x[0],
-                "R1 [Ohm]": x[1],
-            }
-        )
+    def get_data(self, model, parameters, x):
+        model.parameters = parameters
         experiment = pybop.Experiment(
             [
                 (
@@ -103,5 +98,5 @@ def getdata(self, model, x):
                 ),
             ]
         )
-        sim = model.predict(experiment=experiment)
+        sim = model.predict(experiment=experiment, inputs=x)
         return sim