diff --git a/collects/data/heap.rkt b/collects/data/heap.rkt
index 28b19c6df1..a83c75a636 100644
--- a/collects/data/heap.rkt
+++ b/collects/data/heap.rkt
@@ -5,8 +5,8 @@
 
 (define MIN-SIZE 4)
 
-(define-struct heap (vec count <=?) #:mutable)
-;; length(vec)/4 <= size <= length(vec)
+(struct heap ([vec #:mutable] [count #:mutable] <=?))
+;; length(vec)/4 <= size <= length(vec), except size >= MIN-SIZE
 ;; size = next available index
 
 ;; A VT is a binary tree represented as a vector.
@@ -52,7 +52,7 @@
           (unless (<=? n-key child-key)
             (vector-set! vec n child-key)
             (vector-set! vec child n-key)
-            (heapify-down vec child size)))))))
+            (heapify-down <=? vec child size)))))))
 
 (define (subheap? <=? vec n size)
   (let ([left (vt-leftchild n)]
@@ -76,10 +76,11 @@
 
 ;; Heaps
 
-(define make-heap*
-  (let ([make-heap
-         (lambda (<=?) (make-heap (make-vector MIN-SIZE #f) 0 <=?))])
-    make-heap))
+(define (make-heap <=?)
+  (heap (make-vector MIN-SIZE #f) 0 <=?))
+
+(define (list->heap <=? lst)
+  (vector->heap <=? (list->vector lst)))
 
 (define (vector->heap <=? vec0 [start 0] [end (vector-length vec0)])
   (define size (- end start))
@@ -89,27 +90,34 @@
   (vector-copy! vec 0 vec0 start end)
   (for ([n (in-range (sub1 size) -1 -1)])
     (heapify-down <=? vec n size))
-  (make-heap vec size <=?))
+  (heap vec size <=?))
 
 (define (heap-copy h)
   (match h
     [(heap vec count <=?)
-     (make-heap (vector-copy vec) count <=?)]))
+     (heap (vector-copy vec) count <=?)]))
 
 (define (heap-add! h . keys)
   (heap-add-all! h (list->vector keys)))
 
 (define (heap-add-all! h keys)
-  (let ([keys (if (list? keys) (list->vector keys) keys)])
+  (let-values ([(keys keys-size)
+                (cond [(list? keys)
+                       (let ([keys-v (list->vector keys)])
+                         (values keys-v (vector-length keys-v)))]
+                      [(vector? keys)
+                       (values keys (vector-length keys))]
+                      [(heap? keys)
+                       (values (heap-vec keys) (heap-count keys))])])
     (match h
       [(heap vec size <=?)
-       (let* ([new-size (+ size (vector-length keys))]
+       (let* ([new-size (+ size keys-size)]
               [vec (if (> new-size (vector-length vec))
                        (let ([vec (grow-vector vec new-size)])
                          (set-heap-vec! h vec)
                          vec)
                        vec)])
-         (vector-copy! vec size keys 0)
+         (vector-copy! vec size keys 0 keys-size)
          (for ([n (in-range size new-size)])
            (heapify-up <=? vec n))
          (set-heap-count! h new-size))])))
@@ -123,7 +131,7 @@
 
 (define (heap-remove-min! h)
   (match h
-    [(heap vec size <+?)
+    [(heap vec size <=?)
      (when (zero? size)
        (error 'heap-remove-min! "empty heap"))
      (heap-remove-index! h 0)]))
@@ -134,7 +142,7 @@
      (unless (< index size)
        (if (zero? size)
            (error 'heap-remove-index!
-                  "index out of bounds (empty heap): ~s" index)
+                  "empty heap: ~s" index)
            (error 'heap-remove-index!
                   "index out of bounds [0,~s]: ~s" (sub1 size) index)))
      (vector-set! vec index (vector-ref vec (sub1 size)))
@@ -156,23 +164,38 @@
             (lambda _ #t)
             (lambda _ #t))))
 
+;; --------
+
+(define (heap-sort! <=? v)
+  ;; to get ascending order, need max-heap, so reverse comparison
+  (define (>=? x y) (<=? y x))
+  (define size (vector-length v))
+  (for ([n (in-range (sub1 size) -1 -1)])
+    (heapify-down >=? v n size))
+  (for ([last (in-range (sub1 size) 0 -1)])
+    (let ([tmp (vector-ref v 0)])
+      (vector-set! v 0 (vector-ref v last))
+      (vector-set! v last tmp))
+    (heapify-down >=? v 0 last)))
+
+(define (heap->vector h)
+  (match h
+    [(heap vec size <=?)
+     (heap-sort! <=? (vector-copy vec 0 size))]))
+
+;; --------
+
 (provide/contract
  [make-heap (-> (-> any/c any/c any/c) heap?)]
  [heap? (-> any/c boolean?)]
  [heap-count (-> heap? exact-nonnegative-integer?)]
- [heap-copy (-> heap? heap?)]
- [vector->heap (-> (-> any/c any/c any/c) vector? heap?)]
  [heap-add! (->* (heap?) () #:rest list? void?)]
- [heap-add-all! (-> heap? (or/c list? vector?) void?)]
+ [heap-add-all! (-> heap? (or/c list? vector? heap?) void?)]
  [heap-min (-> heap? any/c)]
  [heap-remove-min! (-> heap? void?)]
- [in-heap (-> heap? sequence?)])
 
-#|
-;; Testing
+ [vector->heap (-> (-> any/c any/c any/c) vector? heap?)]
+ [heap->vector (-> heap? vector?)]
+ [heap-copy (-> heap? heap?)]
 
-(vector->heap #(3 65 3 54 3 2 1 4 6))
-
-(define h
-  (vector->heap #(3 65 3 3 2 1)))
-|#
+ [heap-sort! (-> procedure? vector? void?)])
diff --git a/collects/data/scribblings/data.scrbl b/collects/data/scribblings/data.scrbl
index bd9132d8be..8fa30e75b9 100644
--- a/collects/data/scribblings/data.scrbl
+++ b/collects/data/scribblings/data.scrbl
@@ -16,6 +16,8 @@ This manual documents data structure libraries available in the
 @;{--------}
 
 @include-section["queue.scrbl"]
+@include-section["gvector.scrbl"]
+@include-section["splay-tree.scrbl"]
 @include-section["skip-list.scrbl"]
 @include-section["interval-map.scrbl"]
-@include-section["gvector.scrbl"]
+@include-section["heap.scrbl"]
diff --git a/collects/data/scribblings/heap.scrbl b/collects/data/scribblings/heap.scrbl
new file mode 100644
index 0000000000..9cc94f82ea
--- /dev/null
+++ b/collects/data/scribblings/heap.scrbl
@@ -0,0 +1,80 @@
+#lang scribble/manual
+@(require scribble/eval
+          (for-label data/heap
+                     racket/contract
+                     racket/base))
+
+@title{Binary Heap}
+
+@(define the-eval (make-base-eval))
+@(the-eval '(require data/heap))
+
+@defmodule[data/heap]
+
+@author[@author+email["Ryan Culpepper" "ryanc@racket-lang.org"]]
+
+Binary heaps are a simple implementation of priority queues.
+
+@defproc[(make-heap [<=? (-> any/c any/c any/c)])
+         heap?]{
+
+Makes a new empty heap.
+}
+
+@defproc[(heap? [x any/c]) boolean?]{
+
+Returns @racket[#t] if @racket[x] is a heap, @racket[#f] otherwise.
+}
+
+@defproc[(heap-count [h heap?]) exact-nonnegative-integer?]{
+
+Returns the number of elements in the heap.
+}
+
+@defproc[(heap-add! [h heap?] [v any/c] ...) void?]{
+
+Adds each @racket[v] to the heap.
+}
+
+@defproc[(heap-add-all! [h heap?] [v (or/c list? vector? heap?)]) void?]{
+
+Adds each element contained in @racket[v] to the heap, leaving
+@racket[v] unchanged.
+}
+
+@defproc[(heap-min [h heap?]) any/c]{
+
+Returns the least element in the heap @racket[h], according to the
+heap's ordering. If the heap is empty, an exception is raised.
+}
+
+@defproc[(heap-remove-min! [h heap?]) void?]{
+
+Removes the least element in the heap @racket[h]. If the heap is
+empty, an exception is raised.
+}
+
+@defproc[(vector->heap [<=? (-> any/c any/c any/c)] [items vector?]) heap?]{
+
+Builds a heap with the elements from @racket[items]. The vector is not
+modified.
+}
+
+@defproc[(heap->vector [h heap?]) vector?]{
+
+Returns a vector containing the elements of heap @racket[h] in the
+heap's order. The heap is not modified.
+}
+
+@defproc[(heap-copy [h heap?]) heap?]{
+
+Makes a copy of heap @racket[h].
+}
+
+
+@;{--------}
+
+@defproc[(heap-sort! [<=? (-> any/c any/c any/c)] [v vector?]) void?]{
+
+Sorts vector @racket[v] using the comparison function @racket[<=?].
+}
diff --git a/collects/data/scribblings/splay-tree.scrbl b/collects/data/scribblings/splay-tree.scrbl
index baecb0d5bd..289363a44b 100644
--- a/collects/data/scribblings/splay-tree.scrbl
+++ b/collects/data/scribblings/splay-tree.scrbl
@@ -90,7 +90,7 @@ adjustment; see @racket[splay-tree-contract!] and
 @defproc[(splay-tree-remove! [s splay-tree?]
                              [key any/c])
          void?]
-@defproc[(splay-tree-count! [s splay-tree?]) exact-nonnegative-integer?]
+@defproc[(splay-tree-count [s splay-tree?]) exact-nonnegative-integer?]
 @defproc[(splay-tree-iterate-first [s splay-tree?])
          (or/c #f splay-tree-iter?)]
 @defproc[(splay-tree-iterate-next [s splay-tree?] [iter splay-tree-iter?])
diff --git a/collects/data/splay-tree.rkt b/collects/data/splay-tree.rkt
index 967bd0ce2e..5766d08029 100644
--- a/collects/data/splay-tree.rkt
+++ b/collects/data/splay-tree.rkt
@@ -533,7 +533,7 @@ In an integer splay tree, keys can be stored relative to their parent nodes.
  [splay-tree-ref
   (->i ([s splay-tree?] [key (s) (key-c s)])
        ([default any/c])
-       [_ (s default) (or/c (key-c s) (lambda (x) (eq? x default)))])]
+       any)]
  [splay-tree-set!
   (->i ([s splay-tree?] [key (s) (key-c s)] [v (s) (val-c s)]) [_ void?])]
  [splay-tree-remove!