diff --git a/tests/integration/test_monte_carlo_thevenin.py b/tests/integration/test_monte_carlo_thevenin.py
index f9d024ed8..e0c5f2d2b 100644
--- a/tests/integration/test_monte_carlo_thevenin.py
+++ b/tests/integration/test_monte_carlo_thevenin.py
@@ -100,6 +100,7 @@ def map_estimate(self, posterior):
             "max_unchanged_iterations": 35,
             "absolute_tolerance": 1e-7,
             "sigma0": [3e-4, 3e-4],
+            "verbose": True,
         }
         optim = pybop.CMAES(posterior, **common_args)
         results = optim.run()
@@ -127,17 +128,18 @@ def test_sampling_thevenin(self, sampler, posterior, map_estimate):
         x0 = np.clip(map_estimate + np.random.normal(0, 1e-3, size=2), 1e-4, 1e-1)
         common_args = {
             "log_pdf": posterior,
-            "chains": 3,
-            "warm_up": 550,
+            "chains": 2,
+            "warm_up": 100,
             "cov0": [2e-3, 2e-3],
-            "max_iterations": 2000,
+            "max_iterations": 1050,
             "x0": x0,
         }
 
         # construct and run
         sampler = sampler(**common_args)
         if isinstance(sampler, SliceRankShrinkingMCMC):
-            sampler._samplers[0].set_hyper_parameters([1e-3])
+            for i, _j in enumerate(sampler._samplers):
+                sampler._samplers[i].set_hyper_parameters([1e-3])
         chains = sampler.run()
 
         # Test PosteriorSummary
@@ -146,7 +148,7 @@ def test_sampling_thevenin(self, sampler, posterior, map_estimate):
         np.testing.assert_array_less(0, ess)
         if not isinstance(sampler, RelativisticMCMC):
             np.testing.assert_array_less(
-                summary.rhat(), 1.2
+                summary.rhat(), 1.5
             )  # Large rhat, to enable faster tests
 
         # Assert both final sample and posterior mean
diff --git a/tests/integration/test_spm_parameterisations.py b/tests/integration/test_spm_parameterisations.py
index 427534522..1e00d7d77 100644
--- a/tests/integration/test_spm_parameterisations.py
+++ b/tests/integration/test_spm_parameterisations.py
@@ -15,7 +15,7 @@ def setup(self):
         self.sigma0 = 0.002
         self.ground_truth = np.clip(
             np.asarray([0.55, 0.55]) + np.random.normal(loc=0.0, scale=0.05, size=2),
-            a_min=0.4,
+            a_min=0.425,
             a_max=0.75,
         )
 
@@ -124,7 +124,7 @@ def optim(self, optimiser, model, parameters, cost, init_soc):
             "max_unchanged_iterations": 55,
             "sigma0": [0.05, 0.05, 1e-3]
             if isinstance(cost, pybop.GaussianLogLikelihood)
-            else 0.02,
+            else 0.05,
         }
 
         if isinstance(cost, pybop.LogPosterior):