diff --git a/arraycontext/container/__init__.py b/arraycontext/container/__init__.py
index 23f980c86eb8c8e7fc8b9ad144112147d0a9d169..53835333aec5fa59f5e1fdc562b1e11421063cd6 100644
--- a/arraycontext/container/__init__.py
+++ b/arraycontext/container/__init__.py
@@ -123,8 +123,9 @@ def serialize_container(ary: ArrayContainer) -> Iterable[Tuple[Any, Any]]:
 
     The order of the components and their identifiers are entirely under
     the control of the container class. However, the order is required to be
-    deterministic, i.e. two calls to :func:`serialize_container` on the same
-    array container should return an iterable with the components in the same
+    deterministic, i.e. two calls to :func:`serialize_container` on
+    array containers of the same types with the same number of
+    sub-arrays should result in an iterable with the keys in the same
     order.
 
     If *ary* is mutable, the serialization function is not required to ensure