diff --git a/torchrl/objectives/utils.py b/torchrl/objectives/utils.py
index 017394de04b..31954005195 100644
--- a/torchrl/objectives/utils.py
+++ b/torchrl/objectives/utils.py
@@ -203,23 +203,37 @@ def __init__(
 
     @property
     def _targets(self):
-        return TensorDict(
-            {name: getattr(self.loss_module, name) for name in self._target_names},
-            [],
-        )
+        targets = self.__dict__.get("_targets_val", None)
+        if targets is None:
+            targets = self.__dict__["_targets_val"] = TensorDict(
+                {name: getattr(self.loss_module, name) for name in self._target_names},
+                [],
+            )
+        return targets
+
+    @_targets.setter
+    def _targets(self, targets):
+        self.__dict__["_targets_val"] = targets
 
     @property
     def _sources(self):
-        return TensorDict(
-            {name: getattr(self.loss_module, name) for name in self._source_names},
-            [],
-        )
+        sources = self.__dict__.get("_sources_val", None)
+        if sources is None:
+            sources = self.__dict__["_sources_val"] = TensorDict(
+                {name: getattr(self.loss_module, name) for name in self._source_names},
+                [],
+            )
+        return sources
+
+    @_sources.setter
+    def _sources(self, sources):
+        self.__dict__["_sources_val"] = sources
 
     def init_(self) -> None:
         if self.initialized:
             warnings.warn("Updated already initialized.")
         found_distinct = False
-        self._distinct = {}
+        self._distinct_and_params = {}
         for key, source in self._sources.items(True, True):
             if not isinstance(key, tuple):
                 key = (key,)
@@ -228,8 +242,12 @@ def init_(self) -> None:
             # for p_source, p_target in zip(source, target):
             if target.requires_grad:
                 raise RuntimeError("the target parameter is part of a graph.")
-            self._distinct[key] = target.data_ptr() != source.data.data_ptr()
-            found_distinct = found_distinct or self._distinct[key]
+            self._distinct_and_params[key] = (
+                target.is_leaf
+                and source.requires_grad
+                and target.data_ptr() != source.data.data_ptr()
+            )
+            found_distinct = found_distinct or self._distinct_and_params[key]
             target.data.copy_(source.data)
         if not found_distinct:
             raise RuntimeError(
@@ -240,6 +258,23 @@ def init_(self) -> None:
                 f"If no target parameter is needed, do not use a target updater such as {type(self)}."
             )
 
+        # filter the target_ out
+        def filter_target(key):
+            if isinstance(key, tuple):
+                return (filter_target(key[0]), *key[1:])
+            return key[7:]
+
+        self._sources = self._sources.select(
+            *[
+                filter_target(key)
+                for (key, val) in self._distinct_and_params.items()
+                if val
+            ]
+        ).lock_()
+        self._targets = self._targets.select(
+            *(key for (key, val) in self._distinct_and_params.items() if val)
+        ).lock_()
+
         self.initialized = True
 
     def step(self) -> None:
@@ -248,19 +283,11 @@ def step(self) -> None:
                 f"{self.__class__.__name__} must be "
                 f"initialized (`{self.__class__.__name__}.init_()`) before calling step()"
             )
-        for key, source in self._sources.items(True, True):
-            if not isinstance(key, tuple):
-                key = (key,)
-            key = ("target_" + key[0], *key[1:])
-            if not self._distinct[key]:
-                continue
-            target = self._targets[key]
+        for key, param in self._sources.items():
+            target = self._targets.get("target_{}".format(key))
             if target.requires_grad:
                 raise RuntimeError("the target parameter is part of a graph.")
-            if target.is_leaf:
-                self._step(source, target)
-            else:
-                target.copy_(source)
+            self._step(param, target)
 
     def _step(self, p_source: Tensor, p_target: Tensor) -> None:
         raise NotImplementedError
@@ -326,8 +353,10 @@ def __init__(
         super(SoftUpdate, self).__init__(loss_module)
         self.eps = eps
 
-    def _step(self, p_source: Tensor, p_target: Tensor) -> None:
-        p_target.data.copy_(p_target.data * self.eps + p_source.data * (1 - self.eps))
+    def _step(
+        self, p_source: Tensor | TensorDictBase, p_target: Tensor | TensorDictBase
+    ) -> None:
+        p_target.data.lerp_(p_source.data, 1 - self.eps)
 
 
 class HardUpdate(TargetNetUpdater):