diff --git a/drjax/_src/impls.py b/drjax/_src/impls.py
index c43d308..4ad412a 100644
--- a/drjax/_src/impls.py
+++ b/drjax/_src/impls.py
@@ -164,7 +164,6 @@ def broadcast_to_placement(
     n_elements = self._placements_to_n_elements[placement]
 
     def single_arg_broadcast(x):
-      unconstrained_tensor = jnp.tile(x, reps=[n_elements] + [1] * len(x.shape))
       if mesh is None:
         logging.warning(
             'No mesh found; defaulting to fully unconstrained broadcast and'
@@ -172,7 +171,7 @@ def single_arg_broadcast(x):
             ' axis %s.',
             placement,
         )
-        return unconstrained_tensor
+        return jnp.broadcast_to(x, (n_elements,) + x.shape)
       else:
         if mesh.are_all_axes_auto:
           if _placement_axis_in_mesh(mesh, placement):
@@ -182,7 +181,9 @@ def single_arg_broadcast(x):
             # the compiler that there are no constraints on this tensor. This
             # will leave the choices in the hands of the compiler.
             pspec = P(*([P.UNCONSTRAINED] * (len(arg.shape) + 1)))
-          return _constrain_alike_if_mesh(mesh, unconstrained_tensor, x, pspec)
+          return _constrain_alike_if_mesh(
+              mesh, jnp.broadcast_to(x, (n_elements,) + x.shape), x, pspec
+          )
         elif mesh.are_all_axes_explicit:
           input_sharding = jax.typeof(x).sharding
           if _placement_axis_in_mesh(mesh, placement):
@@ -195,8 +196,8 @@ def single_arg_broadcast(x):
             out_sharding = jax.sharding.NamedSharding(
                 input_sharding.mesh, P(None, *input_sharding.spec)
             )
-          return jax.sharding.reshard(
-              unconstrained_tensor, out_shardings=out_sharding
+          return jnp.broadcast_to(
+              x, (n_elements,) + x.shape, out_sharding=out_sharding
           )
         else:
           raise ValueError(
@@ -204,7 +205,7 @@ def single_arg_broadcast(x):
               f' {mesh.axis_types}.'
           )
 
-    return jax.jit(single_arg_broadcast)(arg)
+    return single_arg_broadcast(arg)
 
   def normalized_broadcast_to_placement(
       self,
@@ -290,9 +291,7 @@ def _constrain_at_placement_with_slices_like(x):
           pspec = P(placement, *([P.UNCONSTRAINED] * (len(x.shape) - 1)))
           return _constrain_alike_if_mesh(mesh, x, x[0], pspec)
 
-        arg = jax.tree_util.tree_map(
-            _constrain_at_placement_with_slices_like, arg
-        )
+        arg = jax.tree.map(_constrain_at_placement_with_slices_like, arg)
         mapped_fn = jax.vmap(
             # We must not have an `axis_name` argument here in order to work
             # with any potential `shard_map` inside of `fn`.
@@ -305,27 +304,27 @@ def _constrain_at_placement_with_slices_like(x):
         # In some cases, vmap may prevent placement sharding from propagating.
         # We ensure placement sharding on the output just in case.
         result = call_jaxpr(mapped_fn, arg)
-        return jax.tree_util.tree_map(
-            _constrain_at_placement_with_slices_like, result
-        )
+        return jax.tree.map(_constrain_at_placement_with_slices_like, result)
       elif mesh.are_all_axes_explicit:
         mapped_fn = jax.vmap(
+            # We must not have an `axis_name` argument here in order to work
+            # with any potential `shard_map` inside of `fn`. `fn` should not
+            # contain collectives that operate over the placement axis.
             fn,
-            axis_name=placement,
             in_axes=0,
             out_axes=0,
         )
         result = call_jaxpr(mapped_fn, arg)
         # Ensure the result is sharded along the placement axis when using
         # explicit axes.
-        return jax.tree_util.tree_map(
-            lambda arr: jax.sharding.reshard(
-                arr,
-                jax.sharding.NamedSharding(
+        return jax.sharding.reshard(
+            result,
+            jax.tree.map(
+                lambda arr: jax.sharding.NamedSharding(
                     mesh, spec=P(placement, *jax.typeof(arr).sharding.spec[1:])
                 ),
+                result,
             ),
-            result,
         )
       else:
         raise ValueError(