diff --git a/arraycontext/container/traversal.py b/arraycontext/container/traversal.py
index 8d371434..2127c5d2 100644
--- a/arraycontext/container/traversal.py
+++ b/arraycontext/container/traversal.py
@@ -480,7 +480,7 @@ def rec_map_reduce_array_container(
 
         or any other such traversal.
     """
-    def rec(_ary: ArrayOrContainerT) -> ArrayOrContainerT:
+    def rec(_ary: ArrayOrContainerT) -> Optional[ArrayOrContainerT]:
         if type(_ary) is leaf_class:
             return map_func(_ary)
         else:
@@ -489,11 +489,22 @@ def rec(_ary: ArrayOrContainerT) -> ArrayOrContainerT:
             except NotAnArrayContainerError:
                 return map_func(_ary)
             else:
-                return reduce_func([
-                    rec(subary) for _, subary in iterable
-                    ])
+                subary_results = [
+                    rec(subary) for _, subary in iterable]
+                filtered_subary_results = [
+                    result for result in subary_results
+                    if result is not None]
+                if len(filtered_subary_results) > 0:
+                    return reduce_func(filtered_subary_results)
+                else:
+                    return None
 
-    return rec(ary)
+    result = rec(ary)
+
+    if result is None:
+        raise ValueError("cannot reduce empty array container")
+
+    return result
 
 
 def rec_multimap_reduce_array_container(
@@ -519,12 +530,23 @@ def rec_multimap_reduce_array_container(
     # NOTE: this wrapper matches the signature of `deserialize_container`
     # to make plugging into `_multimap_array_container_impl` easier
     def _reduce_wrapper(ary: ContainerT, iterable: Iterable[Tuple[Any, Any]]) -> Any:
-        return reduce_func([subary for _, subary in iterable])
+        filtered_subary_results = [
+            result for _, result in iterable
+            if result is not None]
+        if len(filtered_subary_results) > 0:
+            return reduce_func(filtered_subary_results)
+        else:
+            return None
 
-    return _multimap_array_container_impl(
+    result = _multimap_array_container_impl(
         map_func, *args,
         reduce_func=_reduce_wrapper, leaf_cls=leaf_class, recursive=True)
 
+    if result is None:
+        raise ValueError("cannot reduce empty array container")
+
+    return result
+
 # }}}