diff --git a/blackjax/smc/tempered.py b/blackjax/smc/tempered.py
index b373d062f..ca41cc39f 100644
--- a/blackjax/smc/tempered.py
+++ b/blackjax/smc/tempered.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+from functools import partial
 from typing import Callable, NamedTuple
 
 import jax
@@ -119,6 +120,13 @@ def kernel(
         """
         delta = lmbda - state.lmbda
 
+        shared_mcmc_parameters = {
+            k: v[0, ...] for k, v in mcmc_parameters.items() if v.shape[0] == 1
+        }
+        unshared_mcmc_parameters = {
+            k: v for k, v in mcmc_parameters.items() if v.shape[0] != 1
+        }
+
         def log_weights_fn(position: ArrayLikeTree) -> float:
             return delta * loglikelihood_fn(position)
 
@@ -127,11 +135,13 @@ def tempered_logposterior_fn(position: ArrayLikeTree) -> float:
             tempered_loglikelihood = state.lmbda * loglikelihood_fn(position)
             return logprior + tempered_loglikelihood
 
+        shared_mcmc_step_fn = partial(mcmc_step_fn, **shared_mcmc_parameters)
+
         def mcmc_kernel(rng_key, position, step_parameters):
             state = mcmc_init_fn(position, tempered_logposterior_fn)
 
             def body_fn(state, rng_key):
-                new_state, info = mcmc_step_fn(
+                new_state, info = shared_mcmc_step_fn(
                     rng_key, state, tempered_logposterior_fn, **step_parameters
                 )
                 return new_state, info
@@ -142,7 +152,7 @@ def body_fn(state, rng_key):
 
         smc_state, info = smc.base.step(
             rng_key,
-            SMCState(state.particles, state.weights, mcmc_parameters),
+            SMCState(state.particles, state.weights, unshared_mcmc_parameters),
             jax.vmap(mcmc_kernel),
             jax.vmap(log_weights_fn),
             resampling_fn,
diff --git a/tests/smc/test_inner_kernel_tuning.py b/tests/smc/test_inner_kernel_tuning.py
index bf970ae47..1ec806063 100644
--- a/tests/smc/test_inner_kernel_tuning.py
+++ b/tests/smc/test_inner_kernel_tuning.py
@@ -281,7 +281,7 @@ def test_with_adaptive_tempered(self):
 
         def parameter_update(state, info):
             return extend_params(
-                100,
+                1,
                 {
                     "inverse_mass_matrix": mass_matrix_from_particles(state.particles),
                     "step_size": 10e-2,
@@ -298,7 +298,7 @@ def parameter_update(state, info):
             resampling.systematic,
             mcmc_parameter_update_fn=parameter_update,
             initial_parameter_value=extend_params(
-                100,
+                1,
                 dict(
                     inverse_mass_matrix=jnp.eye(2),
                     step_size=10e-2,
@@ -326,7 +326,7 @@ def body(carry):
 
         _, state = inference_loop(smc_kernel, self.key, init_state)
 
-        assert state.parameter_override["inverse_mass_matrix"].shape == (100, 2, 2)
+        assert state.parameter_override["inverse_mass_matrix"].shape == (1, 2, 2)
         self.assert_linear_regression_test_case(state.sampler_state)
 
     @chex.all_variants(with_pmap=False)
@@ -340,7 +340,7 @@ def test_with_tempered_smc(self):
 
         def parameter_update(state, info):
             return extend_params(
-                100,
+                1,
                 {
                     "inverse_mass_matrix": mass_matrix_from_particles(state.particles),
                     "step_size": 10e-2,
@@ -357,7 +357,7 @@ def parameter_update(state, info):
             resampling.systematic,
             mcmc_parameter_update_fn=parameter_update,
             initial_parameter_value=extend_params(
-                100,
+                1,
                 dict(
                     inverse_mass_matrix=jnp.eye(2),
                     step_size=10e-2,
diff --git a/tests/smc/test_tempered_smc.py b/tests/smc/test_tempered_smc.py
index a7d9acdd8..dac590a09 100644
--- a/tests/smc/test_tempered_smc.py
+++ b/tests/smc/test_tempered_smc.py
@@ -65,16 +65,25 @@ def logprior_fn(x):
 
         hmc_kernel = blackjax.hmc.build_kernel()
         hmc_init = blackjax.hmc.init
-        hmc_parameters = extend_params(
-            num_particles,
-            {
-                "step_size": 10e-2,
-                "inverse_mass_matrix": jnp.eye(2),
-                "num_integration_steps": 50,
-            },
+        hmc_parameters_list = [
+            extend_params(
+                num_particles if extend else 1,
+                {
+                    "step_size": 10e-2,
+                    "inverse_mass_matrix": jnp.eye(2),
+                    "num_integration_steps": 50,
+                },
+            )
+            for extend in [True, False]
+        ]
+        hmc_parameters_list.append(
+            extend_params(
+                num_particles, {"step_size": 10e-2, "num_integration_steps": 50}
+            )
+            | extend_params(num_particles, {"inverse_mass_matrix": jnp.eye(2)})
         )
 
-        for target_ess in [0.5, 0.75]:
+        for target_ess, hmc_parameters in zip([0.5, 0.5, 0.75], hmc_parameters_list):
             tempering = adaptive_tempered_smc(
                 logprior_fn,
                 loglikelihood_fn,
@@ -115,7 +124,7 @@ def test_fixed_schedule_tempered_smc(self):
         hmc_init = blackjax.hmc.init
         hmc_kernel = blackjax.hmc.build_kernel()
         hmc_parameters = extend_params(
-            100,
+            1,
             {
                 "step_size": 10e-2,
                 "inverse_mass_matrix": jnp.eye(2),