diff --git a/lib/dicthf.gi b/lib/dicthf.gi
index 5ee7341589..819431548a 100644
--- a/lib/dicthf.gi
+++ b/lib/dicthf.gi
@@ -152,16 +152,20 @@ end);
 ##
 InstallMethod(SparseIntKey,"for bounded tuples",true,
     [ IsList,IsList and IsCyclotomicCollection ], 0,
-function(m,v)
-local c;
-  if Length(m)<>3 or m[1]<>"BoundedTuples" then
+function(m, v)
+  if Length(m) <> 3 or m[1] <> "BoundedTuples" then
     TryNextMethod();
   fi;
-  c:=[1,Maximum(m[2])+1];
-  return function(a)
-    return a*c;
+  # Due to the way BoundedTuples are presently implemented we expect the input
+  # to the hash function to always be a list of positive immediate integers. This means
+  # that using HashKeyWholeBag should be safe.
+  return function(x)
+    Assert(1, IsPositionsList(x));
+    if not IsPlistRep(x) then
+      x := AsPlist(x);
+    fi;
+    return HashKeyWholeBag(x, 1);
   end;
-
 end);
 
 BindGlobal( "SparseIntKeyVecListAndMatrix", function(d,m)
diff --git a/tst/teststandard/hash2.tst b/tst/teststandard/hash2.tst
index 6bfa4d3967..d47452e5c7 100644
--- a/tst/teststandard/hash2.tst
+++ b/tst/teststandard/hash2.tst
@@ -32,4 +32,8 @@ gap> Length(Orbit(h,h.1[1],OnRight));
 2079
 gap> Length(Orbit(h,h.2^5,OnPoints));
 693
+gap> Length(Orbit(SymmetricGroup(14), [1 .. 7], OnSets));
+3432
+gap> Length(Orbit(SymmetricGroup(16), [1 .. 8], OnSets));
+12870
 gap> STOP_TEST( "hash2.tst", 1);