diff --git a/src/_zkapauthorizer/foolscap.py b/src/_zkapauthorizer/foolscap.py
index 4e77b5a5075ec4b215d221cbbb8c9e941401cf29..52a43c6daea142758e1fd8b40a727d9b7e21fe9d 100644
--- a/src/_zkapauthorizer/foolscap.py
+++ b/src/_zkapauthorizer/foolscap.py
@@ -125,7 +125,10 @@ class RIPrivacyPassAuthorizedStorageServer(RemoteInterface):
 
     def share_sizes(
             storage_index_or_slot=StorageIndex,
-            sharenums=ChoiceOf(None, SetOf(int, maxLength=MAX_BUCKETS)),
+            # Notionally, ChoiceOf(None, SetOf(int, maxLength=MAX_BUCKETS)).
+            # However, support for such a construction appears to be
+            # unimplemented in Foolscap.  So, instead...
+            sharenums=Any(),
     ):
         """
         Get the size of the given shares in the given storage index or slot.  If a