Matt W answers;
Take advantage of the dynamic function construction in AS3.
private function myCallbackFunction(e:Event, parameter:String):void
{
//voila, here's your parameter
}
private function addArguments(method:Function, additionalArguments:Array):Function
{
return function(event:Event):void {method.apply(null, [event].concat(additionalArguments));}
}
var parameter:String = "A sentence I want to pass along";
movieClip.addEventListener(Event.COMPLETE, addArguments(myCallbackFunction, [parameter] ) );