diff --git a/generic.rkt b/generic.rkt
index ccfb928..44763f7 100644
--- a/generic.rkt
+++ b/generic.rkt
@@ -11,11 +11,25 @@
  ;; Generics
  gen:dds
  ;; Functions
- (contract-out [dds-step-one (-> dds? any/c (set/c any/c))])
+ (contract-out [dds-step-one (-> dds? any/c (set/c any/c))]
+               [dds-step (-> dds? (set/c any/c) (set/c any/c))])
  ;; Predicates
  (contract-out [dds? (-> any/c boolean?)]))
 
+;;; Given a dds and a set of starting states, produce the set of
+;;; states reachable in one step.  This is a fallback for dds-step.
+(define (fallback-dds-step dds ss)
+  (list->set (flatten (for/list ([s ss]) (dds-step-one dds s)))))
+
 ;;; A discrete dynamical system.
 (define-generics dds
   ;; Given a dds and a state, produce the next states of the dds.
-  (dds-step-one dds state))
+  (dds-step-one dds state)
+  ;; Given a dds and a set of starting states, produce the set of
+  ;; states reachable in one step.  This method falls back to running
+  ;; dds-step-one for all states.
+  (dds-step dds states)
+
+  #:defined-predicate dds-implements?
+  #:fallbacks
+  [(define dds-step fallback-dds-step)])
diff --git a/networks-tests.rkt b/networks-tests.rkt
index cb1bc72..ce91a36 100644
--- a/networks-tests.rkt
+++ b/networks-tests.rkt
@@ -113,5 +113,9 @@
          [syn (make-syn-dynamics n)]
          [s (st '((a . #t) (b . #f)))])
     (check-equal? (dds-step-one asyn s) (set (st '((a . #f) (b . #f)))
-                                         (st '((a . #t) (b . #f)))))
-    (check-equal? (dds-step-one syn s) (set (st '((a . #f) (b . #f)))))))
+                                             (st '((a . #t) (b . #f)))))
+    (check-equal? (dds-step-one syn s) (set (st '((a . #f) (b . #f)))))
+    (check-equal? (dds-step asyn (set (st '((a . #t) (b . #t)))
+                                      (st '((a . #f) (b . #t)))))
+                  (set (st '((a . #f) (b . #t)))
+                       (st '((a . #t) (b . #t)))))))
diff --git a/networks.rkt b/networks.rkt
index 1032bcb..02e7b90 100644
--- a/networks.rkt
+++ b/networks.rkt
@@ -36,7 +36,8 @@
                [make-dynamics-from-func (-> network? (-> (listof variable?) mode?) dynamics?)]
                [make-asyn-dynamics (-> network? dynamics?)]
                [make-syn-dynamics (-> network? dynamics?)]
-               [dds-step-one (-> dynamics? state? (set/c state?))])
+               [dds-step-one (-> dynamics? state? (set/c state?))]
+               [dds-step (-> dynamics? (set/c state?) (set/c state?))])
  ;; Predicates
  (contract-out [variable? (-> any/c boolean?)]
                [state? (-> any/c boolean?)]