diff --git a/collects/data/queue.rkt b/collects/data/queue.rkt
index 6095f4a20c..0441541439 100644
--- a/collects/data/queue.rkt
+++ b/collects/data/queue.rkt
@@ -30,8 +30,13 @@
 (define (dequeue! q)
   (unless (queue? q) (raise-type-error dequeue! "queue" 0 q))
   (let ([old (queue-head q)])
-    (unless old (error 'dequeue! "empty queue"))
-    (set-queue-head! q (link-tail old))
+    (unless old (raise-type-error 'dequeue! "non-empty queue" 0 q))
+    (cond
+      [(eq? old (queue-tail q))
+       (set-queue-tail! q #f)
+       (set-queue-head! q #f)]
+      [else
+       (set-queue-head! q (link-tail old))])
     (link-value old)))
 
 (define (queue->list queue)
diff --git a/collects/tests/data/queue.rkt b/collects/tests/data/queue.rkt
index 1a306cd04f..69bd421f3e 100644
--- a/collects/tests/data/queue.rkt
+++ b/collects/tests/data/queue.rkt
@@ -63,7 +63,19 @@
          (enqueue! q 2)
          (check-equal? (dequeue! q) 1)
          (check-equal? (dequeue! q) 2)
-         (check-exn exn:fail? (lambda () (dequeue! q))))))
+         (check-exn exn:fail? (lambda () (dequeue! q)))))
+     (test-case "don't leak last element"
+       (let* ([thing (box 'box-that-queue-should-not-hold-onto)]
+              [wb (make-weak-box thing)]
+              [q (make-queue)])
+         (enqueue! q thing)
+         (set! thing #f)
+         (dequeue! q)
+         (collect-garbage)
+         (check-false (weak-box-value wb))
+         ;; need a reference to 'q' after looking in the
+         ;; box or else the whole queue gets collected
+         (check-true (queue? q)))))
    (test-suite "queue misc"
      (test-case "queue as a sequence"
        (let ([queue (make-queue)])