diff --git a/syndicate/skeleton.rkt b/syndicate/skeleton.rkt
index 6c37da3..2453f5f 100644
--- a/syndicate/skeleton.rkt
+++ b/syndicate/skeleton.rkt
@@ -185,7 +185,7 @@
       [other (values #f other)])))
 
 (define (extend-skeleton! sk desc)
-  (define (walk-node! path sk pop-count index desc)
+  (define (walk-node! rev-path sk pop-count index desc)
     (match desc
       [(list class-desc pieces ...)
        (define class
@@ -203,23 +203,23 @@
        (define (make-skeleton-node-with-cache)
          (define unfiltered (skeleton-continuation-cache (skeleton-node-continuation sk)))
          (define filtered (make-hash))
+         (define path (reverse rev-path))
          (hash-for-each unfiltered
                         (lambda (a _)
                           (when (subterm-matches-class? a path class)
                             (hash-set! filtered a #t))))
          (make-empty-skeleton/cache filtered))
        (define next (hash-ref! table class make-skeleton-node-with-cache))
-       (walk-edge! (append path '(0)) next 0 0 pieces)]
+       (walk-edge! (cons 0 rev-path) next 0 0 pieces)]
       [_
        (values pop-count sk)]))
-  (define (walk-edge! path sk pop-count index pieces)
+  (define (walk-edge! rev-path sk pop-count index pieces)
     (match pieces
       ['()
        (values (+ pop-count 1) sk)]
       [(cons p pieces)
-       (let-values (((pop-count sk) (walk-node! path sk pop-count index p)))
-         (define next-path (append (drop-right path 1) (list (+ index 1))))
-         (walk-edge! next-path sk pop-count (+ index 1) pieces))]))
+       (let-values (((pop-count sk) (walk-node! rev-path sk pop-count index p)))
+         (walk-edge! (cons (+ index 1) (cdr rev-path)) sk pop-count (+ index 1) pieces))]))
   (let-values (((_pop-count sk) (walk-node! '() sk 0 0 desc)))
     sk))