diff --git a/module/language/cps/contification.scm b/module/language/cps/contification.scm
index 970432adf..aa162e021 100644
--- a/module/language/cps/contification.scm
+++ b/module/language/cps/contification.scm
@@ -30,7 +30,7 @@
 
 (define-module (language cps contification)
   #:use-module (ice-9 match)
-  #:use-module ((srfi srfi-1) #:select (concatenate))
+  #:use-module ((srfi srfi-1) #:select (concatenate filter-map))
   #:use-module (srfi srfi-26)
   #:use-module (language cps)
   #:use-module (language cps dfg)
@@ -49,8 +49,8 @@
       (set! call-substs (acons sym (map cons arities body-ks) call-substs)))
     (define (subst-return! old-tail new-tail)
       (set! cont-substs (acons old-tail new-tail cont-substs)))
-    (define (elide-function! k)
-      (set! fun-elisions (cons k fun-elisions)))
+    (define (elide-function! k cont)
+      (set! fun-elisions (acons k cont fun-elisions)))
     (define (splice-conts! scope conts)
       (hashq-set! cont-splices scope
                   (append conts (hashq-ref cont-splices scope '()))))
@@ -230,7 +230,7 @@
             (if (and=> (bound-symbol k)
                        (lambda (sym)
                          (contify-fun term-k sym self tail-k arity body)))
-                (elide-function! k)
+                (elide-function! k (lookup-cont k cont-table))
                 (visit-fun exp)))
            (_ #t)))))
 
@@ -276,10 +276,10 @@
            (($ $letrec names syms funs body)
             ($letrec names syms funs ,(lp body)))
            (($ $letk conts* body)
-            ($letk ,(append conts* (map visit-cont cont))
+            ($letk ,(append conts* (filter-map visit-cont cont))
               ,body))
            (body
-            ($letk ,(map visit-cont cont)
+            ($letk ,(filter-map visit-cont cont)
               ,body)))))))
   (define (visit-fun term)
     (rewrite-cps-exp term
@@ -287,9 +287,9 @@
        ($fun meta free ,(visit-cont body)))))
   (define (visit-cont cont)
     (rewrite-cps-cont cont
-      (($ $cont (and k (? (cut memq <> fun-elisions))) src
-          ($ $kargs (_) (_) body))
-       (k src ($kargs () () ,(visit-term body k))))
+      (($ $cont (? (cut assq <> fun-elisions)))
+       ;; This cont gets inlined in place of the $fun.
+       ,#f)
       (($ $cont sym src ($ $kargs names syms body))
        (sym src ($kargs names syms ,(visit-term body sym))))
       (($ $cont sym src ($ $kentry self tail clauses))
@@ -312,10 +312,10 @@
            (($ $letrec names syms funs body)
             ($letrec names syms funs ,(lp body)))
            (($ $letk conts* body)
-            ($letk ,(append conts* (map visit-cont conts))
+            ($letk ,(append conts* (filter-map visit-cont conts))
               ,body))
            (body
-            ($letk ,(map visit-cont conts)
+            ($letk ,(filter-map visit-cont conts)
               ,body)))))
       (($ $letrec names syms funs body)
        (rewrite-cps-term (filter (match-lambda
@@ -329,10 +329,13 @@
         term-k
         (match exp
           (($ $fun)
-           (if (memq k fun-elisions)
-               (build-cps-term
-                 ($continue k ($values ())))
-               (continue k (visit-fun exp))))
+           (cond
+            ((assq-ref fun-elisions k)
+             => (match-lambda
+                 (($ $kargs (_) (_) body)
+                  (visit-term body k))))
+            (else
+             (continue k (visit-fun exp)))))
           (($ $call proc args)
            (or (contify-call proc args)
                (continue k exp)))