--- a/testing/mochitest/tests/SimpleTest/specialpowersAPI.js
+++ b/testing/mochitest/tests/SimpleTest/specialpowersAPI.js
@@ -151,30 +151,38 @@ function isXrayWrapper(x) {
 }
 
 // We can't call apply() directy on Xray-wrapped functions, so we have to be
 // clever.
 function doApply(fun, invocant, args) {
   return Function.prototype.apply.call(fun, invocant, args);
 }
 
+// Use a weak map to cache wrappers. This allows the wrappers to preserve identity.
+var wrapperCache = WeakMap();
+
 function wrapPrivileged(obj) {
 
   // Primitives pass straight through.
   if (!isWrappable(obj))
     return obj;
 
   // No double wrapping.
   if (isWrapper(obj))
     throw "Trying to double-wrap object!";
 
+  // Try the cache.
+  if (wrapperCache.has(obj))
+    return wrapperCache.get(obj);
+
   // Make our core wrapper object.
   var handler = new SpecialPowersHandler(obj);
 
   // If the object is callable, make a function proxy.
+  var wrapper;
   if (typeof obj === "function") {
     var callTrap = function() {
       // The invocant and arguments may or may not be wrappers. Unwrap them if necessary.
       var invocant = unwrapIfWrapped(this);
       var unwrappedArgs = Array.prototype.slice.call(arguments).map(unwrapIfWrapped);
 
       return wrapPrivileged(doApply(obj, invocant, unwrappedArgs));
     };
@@ -188,21 +196,26 @@ function wrapPrivileged(obj) {
       var FakeConstructor = function() {
         doApply(obj, this, unwrappedArgs);
       };
       FakeConstructor.prototype = obj.prototype;
 
       return wrapPrivileged(new FakeConstructor());
     };
 
-    return Proxy.createFunction(handler, callTrap, constructTrap);
+    wrapper = Proxy.createFunction(handler, callTrap, constructTrap);
+  }
+  // Otherwise, just make a regular object proxy.
+  else {
+    wrapper = Proxy.create(handler);
   }
 
-  // Otherwise, just make a regular object proxy.
-  return Proxy.create(handler);
+  // Cache the wrapper and return it.
+  wrapperCache.set(obj, wrapper);
+  return wrapper;
 };
 
 function unwrapPrivileged(x) {
 
   // We don't wrap primitives, so sometimes we have a primitive where we'd
   // expect to have a wrapper. The proxy pretends to be the type that it's
   // emulating, so we can just as easily check isWrappable() on a proxy as
   // we can on an unwrapped object.
@@ -403,19 +416,16 @@ SpecialPowersAPI.prototype = {
    * object containing a reference to the underlying object, where all method
    * calls and property accesses are transparently performed with the System
    * Principal. Moreover, objects obtained from the wrapper (including properties
    * and method return values) are wrapped automatically. Thus, after a single
    * call to SpecialPowers.wrap(), the wrapper layer is transitively maintained.
    *
    * Known Issues:
    *
-   *  - The wrapping function does not preserve identity, so
-   *    SpecialPowers.wrap(foo) !== SpecialPowers.wrap(foo). See bug 718543.
-   *
    *  - The wrapper cannot see expando properties on unprivileged DOM objects.
    *    That is to say, the wrapper uses Xray delegation.
    *
    *  - The wrapper sometimes guesses certain ES5 attributes for returned
    *    properties. This is explained in a comment in the wrapper code above,
    *    and shouldn't be a problem.
    */
   wrap: wrapPrivileged,

--- a/testing/mochitest/tests/test_SpecialPowersExtension.html
+++ b/testing/mochitest/tests/test_SpecialPowersExtension.html
@@ -129,16 +129,23 @@ function starttest(){
   noxray.__proto__ = noxray_proto;
   var noxray_wrapper = SpecialPowers.wrap(noxray);
   is(noxray_wrapper.c, 32, "Regular properties should work.");
   is(noxray_wrapper.a, 5, "Shadow properties should work.");
   is(noxray_wrapper.b, 12, "Proto properties should work.");
   noxray.b = 122;
   is(noxray_wrapper.b, 122, "Should be able to shadow.");
 
+  // Check that the wrapper preserves identity.
+  var someIdentityObject = {a: 2};
+  ok(SpecialPowers.wrap(someIdentityObject) === SpecialPowers.wrap(someIdentityObject),
+     "SpecialPowers wrapping should preserve identity!");
+  ok(webnav === SpecialPowers.wrap(SpecialPowers.unwrap(webnav)),
+     "SpecialPowers wrapping should preserve identity!");
+
   info("\nProfile::SpecialPowersRunTime: " + (new Date() - startTime) + "\n");
   SimpleTest.finish();
 }
 </script>
 </pre>
 </body>
 </html>