diff --git a/src/array_api_extra/_lib/_utils/_helpers.py b/src/array_api_extra/_lib/_utils/_helpers.py
index 99fcf65a..b856eb41 100644
--- a/src/array_api_extra/_lib/_utils/_helpers.py
+++ b/src/array_api_extra/_lib/_utils/_helpers.py
@@ -463,7 +463,7 @@ def pickle_unflatten(instances: Iterable[object], rest: FlattenRest) -> Any:  #
     Notes
     -----
     The `instances` iterable must yield at least the same number of elements as the ones
-    returned by ``pickle_without``, but the elements do not need to be the same objects
+    returned by ``pickle_flatten``, but the elements do not need to be the same objects
     or even the same types of objects. Excess elements, if any, will be left untouched.
     """
     iters = iter(instances), iter(rest)
@@ -540,6 +540,25 @@ def jax_autojit(
     See Also
     --------
     jax.jit : JAX JIT compilation function.
+
+    Notes
+    -----
+    These are useful choices *for testing purposes only*, which is how this function is
+    intended to be used. The output of ``jax.jit`` is a C++ level callable, that
+    directly dispatches to the compiled kernel after the initial call. In comparison,
+    ``jax_autojit`` incurs a much higher dispatch time.
+
+    Additionally, consider::
+
+        def f(x: Array, y: float, plus: bool) -> Array:
+            return x + y if plus else x - y
+
+        j1 = jax.jit(f, static_argnames="plus")
+        j2 = jax_autojit(f)
+
+    In the above example, ``j2`` requires a lot less setup to be tested effectively than
+    ``j1``, but on the flip side it means that it will be re-traced for every different
+    value of ``y``, which likely makes it not fit for purpose in production.
     """
     import jax
 
diff --git a/src/array_api_extra/testing.py b/src/array_api_extra/testing.py
index c14e9a22..3979f9dd 100644
--- a/src/array_api_extra/testing.py
+++ b/src/array_api_extra/testing.py
@@ -96,6 +96,7 @@ def lazy_xp_function(  # type: ignore[explicit-any]
     jax_jit : bool, optional
         Set to True to replace `func` with a smart variant of ``jax.jit(func)`` after
         calling the :func:`patch_lazy_xp_functions` test helper with ``xp=jax.numpy``.
+        This is the default behaviour.
         Set to False if `func` is only compatible with eager (non-jitted) JAX.
 
         Unlike with vanilla ``jax.jit``, all arguments and return types that are not JAX