diff --git a/blackjax/adaptation/adjusted_mclmc_adaptation.py b/blackjax/adaptation/adjusted_mclmc_adaptation.py
index eabb642a3..408c31383 100644
--- a/blackjax/adaptation/adjusted_mclmc_adaptation.py
+++ b/blackjax/adaptation/adjusted_mclmc_adaptation.py
@@ -79,9 +79,15 @@ def adjusted_mclmc_find_L_and_step_size(
 
     part1_key, part2_key = jax.random.split(rng_key, 2)
 
+    total_num_tuning_integrator_steps = 0
     for i in range(num_windows):
         window_key = jax.random.fold_in(part1_key, i)
-        (state, params, eigenvector) = adjusted_mclmc_make_L_step_size_adaptation(
+        (
+            state,
+            params,
+            eigenvector,
+            num_tuning_integrator_steps,
+        ) = adjusted_mclmc_make_L_step_size_adaptation(
             kernel=mclmc_kernel,
             dim=dim,
             frac_tune1=frac_tune1,
@@ -90,22 +96,38 @@ def adjusted_mclmc_find_L_and_step_size(
             diagonal_preconditioning=diagonal_preconditioning,
             max=max,
             tuning_factor=tuning_factor,
-        )(state, params, num_steps, window_key)
+        )(
+            state, params, num_steps, window_key
+        )
+        total_num_tuning_integrator_steps += num_tuning_integrator_steps
 
     if frac_tune3 != 0:
         for i in range(num_windows):
             part2_key = jax.random.fold_in(part2_key, i)
             part2_key1, part2_key2 = jax.random.split(part2_key, 2)
 
-            state, params = adjusted_mclmc_make_adaptation_L(
+            (
+                state,
+                params,
+                num_tuning_integrator_steps,
+            ) = adjusted_mclmc_make_adaptation_L(
                 mclmc_kernel,
                 frac=frac_tune3,
                 Lfactor=0.5,
                 max=max,
                 eigenvector=eigenvector,
-            )(state, params, num_steps, part2_key1)
+            )(
+                state, params, num_steps, part2_key1
+            )
 
-            (state, params, _) = adjusted_mclmc_make_L_step_size_adaptation(
+            total_num_tuning_integrator_steps += num_tuning_integrator_steps
+
+            (
+                state,
+                params,
+                _,
+                num_tuning_integrator_steps,
+            ) = adjusted_mclmc_make_L_step_size_adaptation(
                 kernel=mclmc_kernel,
                 dim=dim,
                 frac_tune1=frac_tune1,
@@ -115,9 +137,13 @@ def adjusted_mclmc_find_L_and_step_size(
                 diagonal_preconditioning=diagonal_preconditioning,
                 max=max,
                 tuning_factor=tuning_factor,
-            )(state, params, num_steps, part2_key2)
+            )(
+                state, params, num_steps, part2_key2
+            )
 
-    return state, params
+            total_num_tuning_integrator_steps += num_tuning_integrator_steps
+
+    return state, params, total_num_tuning_integrator_steps
 
 
 def adjusted_mclmc_make_L_step_size_adaptation(
@@ -256,6 +282,7 @@ def L_step_size_adaptation(state, params, num_steps, rng_key):
             update_da=update_da,
         )
 
+        num_tuning_integrator_steps = info.num_integration_steps.sum()
         final_stepsize = final_da(dual_avg_state)
         params = params._replace(step_size=final_stepsize)
 
@@ -299,9 +326,11 @@ def L_step_size_adaptation(state, params, num_steps, rng_key):
                 initial_da=initial_da,
             )
 
+            num_tuning_integrator_steps += info.num_integration_steps.sum()
+
             params = params._replace(step_size=final_da(dual_avg_state))
 
-        return state, params, eigenvector
+        return state, params, eigenvector, num_tuning_integrator_steps
 
     return L_step_size_adaptation
 
@@ -316,16 +345,16 @@ def adaptation_L(state, params, num_steps, key):
         adaptation_L_keys = jax.random.split(key, num_steps)
 
         def step(state, key):
-            next_state, _ = kernel(
+            next_state, info = kernel(
                 rng_key=key,
                 state=state,
                 step_size=params.step_size,
                 avg_num_integration_steps=params.L / params.step_size,
                 inverse_mass_matrix=params.inverse_mass_matrix,
             )
-            return next_state, next_state.position
+            return next_state, (next_state.position, info)
 
-        state, samples = jax.lax.scan(
+        state, (samples, info) = jax.lax.scan(
             f=step,
             init=state,
             xs=adaptation_L_keys,
@@ -346,10 +375,14 @@ def step(state, key):
         # number of effective samples per 1 actual sample
         ess = contract(effective_sample_size(flat_samples[None, ...])) / num_steps
 
-        return state, params._replace(
-            L=jnp.clip(
-                Lfactor * params.L / jnp.mean(ess), max=params.L * Lratio_upperbound
-            )
+        return (
+            state,
+            params._replace(
+                L=jnp.clip(
+                    Lfactor * params.L / jnp.mean(ess), max=params.L * Lratio_upperbound
+                )
+            ),
+            info.num_integration_steps.sum(),
         )
 
     return adaptation_L
diff --git a/blackjax/adaptation/mclmc_adaptation.py b/blackjax/adaptation/mclmc_adaptation.py
index aa192b964..60fd46359 100644
--- a/blackjax/adaptation/mclmc_adaptation.py
+++ b/blackjax/adaptation/mclmc_adaptation.py
@@ -126,7 +126,7 @@ def mclmc_find_L_and_step_size(
             mclmc_kernel(params.inverse_mass_matrix), frac=frac_tune3, Lfactor=0.4
         )(state, params, num_steps, part2_key)
 
-    return state, params
+    return state, params, num_steps * (frac_tune1 + frac_tune2 + frac_tune3)
 
 
 def make_L_step_size_adaptation(
@@ -274,8 +274,8 @@ def make_adaptation_L(kernel, frac, Lfactor):
     """determine L by the autocorrelations (around 10 effective samples are needed for this to be accurate)"""
 
     def adaptation_L(state, params, num_steps, key):
-        num_steps = int(num_steps * frac)
-        adaptation_L_keys = jax.random.split(key, num_steps)
+        num_steps_3 = int(num_steps * frac)
+        adaptation_L_keys = jax.random.split(key, num_steps_3)
 
         def step(state, key):
             next_state, _ = kernel(
@@ -297,7 +297,7 @@ def step(state, key):
         ess = effective_sample_size(flat_samples[None, ...])
 
         return state, params._replace(
-            L=Lfactor * params.step_size * jnp.mean(num_steps / ess)
+            L=Lfactor * params.step_size * jnp.mean(num_steps_3 / ess)
         )
 
     return adaptation_L
diff --git a/tests/mcmc/test_sampling.py b/tests/mcmc/test_sampling.py
index 34c2e3010..4d8a9fa61 100644
--- a/tests/mcmc/test_sampling.py
+++ b/tests/mcmc/test_sampling.py
@@ -122,6 +122,7 @@ def run_mclmc(
         (
             blackjax_state_after_tuning,
             blackjax_mclmc_sampler_params,
+            _,
         ) = blackjax.mclmc_find_L_and_step_size(
             mclmc_kernel=kernel,
             num_steps=num_steps,
@@ -183,6 +184,7 @@ def run_adjusted_mclmc(
         (
             blackjax_state_after_tuning,
             blackjax_mclmc_sampler_params,
+            _,
         ) = blackjax.adjusted_mclmc_find_L_and_step_size(
             mclmc_kernel=kernel,
             num_steps=num_steps,
@@ -252,6 +254,7 @@ def run_adjusted_mclmc_static(
         (
             blackjax_state_after_tuning,
             blackjax_mclmc_sampler_params,
+            _,
         ) = blackjax.adjusted_mclmc_find_L_and_step_size(
             mclmc_kernel=kernel,
             num_steps=num_steps,
@@ -509,10 +512,7 @@ def get_inverse_mass_matrix():
                 inverse_mass_matrix=inverse_mass_matrix,
             )
 
-            (
-                _,
-                blackjax_mclmc_sampler_params,
-            ) = blackjax.mclmc_find_L_and_step_size(
+            (_, blackjax_mclmc_sampler_params, _) = blackjax.mclmc_find_L_and_step_size(
                 mclmc_kernel=kernel,
                 num_steps=num_steps,
                 state=initial_state,