diff --git a/torchrl/_utils.py b/torchrl/_utils.py
index d37aebb862f..c81ffcc962b 100644
--- a/torchrl/_utils.py
+++ b/torchrl/_utils.py
@@ -829,6 +829,7 @@ def _can_be_pickled(obj):
 def _make_ordinal_device(device: torch.device):
     if device is None:
         return device
+    device = torch.device(device)
     if device.type == "cuda" and device.index is None:
         return torch.device("cuda", index=torch.cuda.current_device())
     if device.type == "mps" and device.index is None:
diff --git a/torchrl/envs/utils.py b/torchrl/envs/utils.py
index d2ec66475ab..f7403e6a69e 100644
--- a/torchrl/envs/utils.py
+++ b/torchrl/envs/utils.py
@@ -14,7 +14,7 @@
 import re
 import warnings
 from enum import Enum
-from typing import Any, Dict, List, Union
+from typing import Any, Dict, List
 
 import torch
 
@@ -339,48 +339,47 @@ def step_mdp(
     exclude_reward: bool = True,
     exclude_done: bool = False,
     exclude_action: bool = True,
-    reward_keys: Union[NestedKey, List[NestedKey]] = "reward",
-    done_keys: Union[NestedKey, List[NestedKey]] = "done",
-    action_keys: Union[NestedKey, List[NestedKey]] = "action",
+    reward_keys: NestedKey | List[NestedKey] = "reward",
+    done_keys: NestedKey | List[NestedKey] = "done",
+    action_keys: NestedKey | List[NestedKey] = "action",
 ) -> TensorDictBase:
     """Creates a new tensordict that reflects a step in time of the input tensordict.
 
     Given a tensordict retrieved after a step, returns the :obj:`"next"` indexed-tensordict.
-    The arguments allow for a precise control over what should be kept and what
+    The arguments allow for precise control over what should be kept and what
     should be copied from the ``"next"`` entry. The default behavior is:
-    move the observation entries, reward and done states to the root, exclude
-    the current action and keep all extra keys (non-action, non-done, non-reward).
+    move the observation entries, reward, and done states to the root, exclude
+    the current action, and keep all extra keys (non-action, non-done, non-reward).
 
     Args:
-        tensordict (TensorDictBase): tensordict with keys to be renamed
-        next_tensordict (TensorDictBase, optional): destination tensordict
-        keep_other (bool, optional): if ``True``, all keys that do not start with :obj:`'next_'` will be kept.
+        tensordict (TensorDictBase): The tensordict with keys to be renamed.
+        next_tensordict (TensorDictBase, optional): The destination tensordict. If `None`, a new tensordict is created.
+        keep_other (bool, optional): If ``True``, all keys that do not start with :obj:`'next_'` will be kept.
             Default is ``True``.
-        exclude_reward (bool, optional): if ``True``, the :obj:`"reward"` key will be discarded
+        exclude_reward (bool, optional): If ``True``, the :obj:`"reward"` key will be discarded
             from the resulting tensordict. If ``False``, it will be copied (and replaced)
-            from the ``"next"`` entry (if present).
-            Default is ``True``.
-        exclude_done (bool, optional): if ``True``, the :obj:`"done"` key will be discarded
+            from the ``"next"`` entry (if present). Default is ``True``.
+        exclude_done (bool, optional): If ``True``, the :obj:`"done"` key will be discarded
             from the resulting tensordict. If ``False``, it will be copied (and replaced)
-            from the ``"next"`` entry (if present).
-            Default is ``False``.
-        exclude_action (bool, optional): if ``True``, the :obj:`"action"` key will
+            from the ``"next"`` entry (if present). Default is ``False``.
+        exclude_action (bool, optional): If ``True``, the :obj:`"action"` key will
             be discarded from the resulting tensordict. If ``False``, it will
             be kept in the root tensordict (since it should not be present in
-            the ``"next"`` entry).
-            Default is ``True``.
-        reward_keys (NestedKey or list of NestedKey, optional): the keys where the reward is written. Defaults
+            the ``"next"`` entry). Default is ``True``.
+        reward_keys (NestedKey or list of NestedKey, optional): The keys where the reward is written. Defaults
             to "reward".
-        done_keys (NestedKey or list of NestedKey, optional): the keys where the done is written. Defaults
+        done_keys (NestedKey or list of NestedKey, optional): The keys where the done is written. Defaults
             to "done".
-        action_keys (NestedKey or list of NestedKey, optional): the keys where the action is written. Defaults
+        action_keys (NestedKey or list of NestedKey, optional): The keys where the action is written. Defaults
             to "action".
 
     Returns:
-         A new tensordict (or next_tensordict) containing the tensors of the t+1 step.
+        TensorDictBase: A new tensordict (or `next_tensordict` if provided) containing the tensors of the t+1 step.
+
+    .. seealso:: :meth:`EnvBase.step_mdp` is the class-based version of this free function. It will attempt to cache the
+        key values to reduce the overhead of making a step in the MDP.
 
     Examples:
-    This funtion allows for this kind of loop to be used:
         >>> from tensordict import TensorDict
         >>> import torch
         >>> td = TensorDict({
@@ -784,8 +783,8 @@ def check_env_specs(
 
     if _has_dynamic_specs(env.specs):
         for real, fake in zip(
-            real_tensordict.filter_non_tensor_data().unbind(-1),
-            fake_tensordict.filter_non_tensor_data().unbind(-1),
+            real_tensordict_select.filter_non_tensor_data().unbind(-1),
+            fake_tensordict_select.filter_non_tensor_data().unbind(-1),
         ):
             fake = fake.apply(lambda x, y: x.expand_as(y), real)
             if (torch.zeros_like(real) != torch.zeros_like(fake)).any():