diff --git a/test/test_env.py b/test/test_env.py
index fc566749b8c..cfe4f04015c 100644
--- a/test/test_env.py
+++ b/test/test_env.py
@@ -1242,7 +1242,7 @@ def test_nested(
         obs_key = "state"
         if nested_obs:
             obs_key = nested_key + (obs_key,)
-        other_key = "beatles"
+        other_key = "other"
         if nested_other:
             other_key = nested_key + (other_key,)
 
@@ -1310,7 +1310,7 @@ def test_nested(
         else:
             assert done_key not in td_nested_keys
         if keep_other:
-            assert other_key in td_nested_keys
+            assert other_key in td_nested_keys, other_key
             assert (td[other_key] == 0).all()
         else:
             assert other_key not in td_nested_keys
diff --git a/torchrl/envs/batched_envs.py b/torchrl/envs/batched_envs.py
index 03262fcdd1d..dd96e2a7a5c 100644
--- a/torchrl/envs/batched_envs.py
+++ b/torchrl/envs/batched_envs.py
@@ -474,6 +474,11 @@ def _create_td(self) -> None:
         # safe since the td is locked.
         self._cache_shared_keys = set(self.shared_tensordict_parent.keys(True, True))
 
+        self._shared_tensordict_parent_next = self.shared_tensordict_parent.get("next")
+        self._shared_tensordict_parent_root = self.shared_tensordict_parent.exclude(
+            "next", *self.reset_keys
+        )
+
     def _start_workers(self) -> None:
         """Starts the various envs."""
         raise NotImplementedError
@@ -862,17 +867,17 @@ def step_and_maybe_reset(
             #   and this transform overrides an observation key (eg, CatFrames)
             #   the shape, dtype or device may not necessarily match and writing
             #   the value in-place will fail.
-            for key in tensordict.keys(True, True):
+            for key in self._env_input_keys:
+                self.shared_tensordict_parent.set_(key, tensordict.get(key))
+            next_td = tensordict.get("next", None)
+            if next_td is not None:
                 # we copy the input keys as well as the keys in the 'next' td, if any
                 # as this mechanism can be used by a policy to set anticipatively the
                 # keys of the next call (eg, with recurrent nets)
-                if key in self._env_input_keys or (
-                    isinstance(key, tuple)
-                    and key[0] == "next"
-                    and key in self.shared_tensordict_parent.keys(True, True)
-                ):
-                    val = tensordict.get(key)
-                    self.shared_tensordict_parent.set_(key, val)
+                for key in next_td.keys(True, True):
+                    key = unravel_key(("next", key))
+                    if key in self.shared_tensordict_parent.keys(True, True):
+                        self.shared_tensordict_parent.set_(key, next_td.get(key[1:]))
         else:
             self.shared_tensordict_parent.update_(
                 tensordict.select(*self._env_input_keys, "next", strict=False)
@@ -887,8 +892,8 @@ def step_and_maybe_reset(
 
         # We must pass a clone of the tensordict, as the values of this tensordict
         # will be modified in-place at further steps
-        next_td = self.shared_tensordict_parent.get("next")
-        tensordict_ = self.shared_tensordict_parent.exclude("next", *self.reset_keys)
+        next_td = self._shared_tensordict_parent_next
+        tensordict_ = self._shared_tensordict_parent_root
         device = self.device
         if self.shared_tensordict_parent.device == device:
             next_td = next_td.clone()
@@ -1201,12 +1206,12 @@ def _run_worker_pipe_shared_mem(
             i = 0
             next_shared_tensordict = shared_tensordict.get("next")
             root_shared_tensordict = shared_tensordict.exclude("next")
-            shared_tensordict = shared_tensordict.clone(False)
-
             if not (shared_tensordict.is_shared() or shared_tensordict.is_memmap()):
                 raise RuntimeError(
                     "tensordict must be placed in shared memory (share_memory_() or memmap_())"
                 )
+            shared_tensordict = shared_tensordict.clone(False)
+
             initialized = True
 
         elif cmd == "reset":
diff --git a/torchrl/envs/utils.py b/torchrl/envs/utils.py
index 6605301ed3b..f505def52af 100644
--- a/torchrl/envs/utils.py
+++ b/torchrl/envs/utils.py
@@ -187,7 +187,7 @@ def step_mdp(
             next_tensordicts = next_tensordict.unbind(tensordict.stack_dim)
         else:
             next_tensordicts = [None] * len(tensordict.tensordicts)
-        out = torch.stack(
+        out = LazyStackedTensorDict.lazy_stack(
             [
                 step_mdp(
                     td,