diff --git a/jax/_src/custom_derivatives.py b/jax/_src/custom_derivatives.py
index ed9b051d5777..4706dfd685f4 100644
--- a/jax/_src/custom_derivatives.py
+++ b/jax/_src/custom_derivatives.py
@@ -43,8 +43,9 @@
 from jax._src.interpreters.batching import not_mapped
 from jax._src.tree_util import (
     tree_flatten, tree_unflatten, tree_map, treedef_is_leaf, treedef_tuple,
-    register_pytree_node_class, tree_leaves, tree_flatten_with_path,
-    tree_leaves_with_path, keystr, treedef_children, tree_structure, PyTreeDef)
+    register_pytree_node_class, tree_leaves, tree_map_with_path,
+    tree_flatten_with_path, tree_leaves_with_path, keystr, treedef_children,
+    tree_structure, PyTreeDef)
 from jax._src.util import (cache, safe_zip, safe_map, split_list, unzip2,
                            weakref_lru_cache)
 
@@ -72,10 +73,15 @@ def _sum_tangents(_, x, *xs):
 def _zeros_like_pytree(x):
   return tree_map(Zero.from_primal_value, x)
 
-_stop_gradient = partial(
-    tree_map,
-    lambda x: stop_gradient_p.bind(x) if isinstance(x, core.Tracer) else x,
-)
+def _check_tracer(i, x):
+  return tree_map_with_path(partial(_check_tracer_, i), x)
+
+def _check_tracer_(i, path, x):
+  if isinstance(x, core.Tracer):
+    pathstr = f' path {keystr(path)}' if path else ''
+    raise Exception(f"Tracer of type {x.aval} passed at argument {i}{pathstr}, "
+                    "but Tracers can't be passed as nondiff_argnums.")
+  return x
 
 
 # like the api_util.py function, but also grabs output avals for error checking
@@ -276,7 +282,7 @@ def __call__(self, *args: Any, **kwargs: Any) -> ReturnValue:  # pytype: disable
       ) from e
 
     if self.nondiff_argnums:
-      args = tuple(_stop_gradient(x) if i in self.nondiff_argnums else x
+      args = tuple(_check_tracer(i, x) if i in self.nondiff_argnums else x
                    for i, x in enumerate(args))
       diff_argnums = [i for i in range(len(args)) if i not in self.nondiff_argnums]
       f_, dyn_args = argnums_partial(lu.wrap_init(self.fun, debug_info=debug),