diff --git a/collects/mred/private/wx/cocoa/const.rkt b/collects/mred/private/wx/cocoa/const.rkt
index d2f99cb3..63e6b8a7 100644
--- a/collects/mred/private/wx/cocoa/const.rkt
+++ b/collects/mred/private/wx/cocoa/const.rkt
@@ -16,8 +16,6 @@
 (define NSRoundedBezelStyle 1)
 (define NSRegularSquareBezelStyle 2)
 
-(define NSAnyEventMask #xffffffff)
-
 (define NSLeftMouseDown 1)
 (define NSLeftMouseUp 2)
 (define NSRightMouseDown 3)
diff --git a/collects/mred/private/wx/cocoa/queue.rkt b/collects/mred/private/wx/cocoa/queue.rkt
index d0ac5d21..67af3656 100644
--- a/collects/mred/private/wx/cocoa/queue.rkt
+++ b/collects/mred/private/wx/cocoa/queue.rkt
@@ -312,6 +312,8 @@
                                (custodian-shutdown-all c)))))))
       (set! was-menu-bar #f)))
 
+(define NSAnyEventMask (sub1 (arithmetic-shift 1 (* 8 (ctype-sizeof _NSUInteger)))))
+
 ;; Call this function only in atomic mode:
 (define (check-one-event wait? dequeue?)
   (pre-event-sync wait?)