Java: How to remove elements from a list while iterating over/adding to it

This question is a more special case of the problem described (and solved) in this question.

I have two methods, stopAndRemove(ServerObject server) and a close() method. The later should close all servers and remove them from the server list. The list is defined as

List<ServerObject> server. 

I do not want to have almost the same code from stopAndRemove in closeCurrentlyOpen, so I want to do something like:

public void closeCurrentlyOpen() {
   for(ServerObject server : this.servers) {
       stopAndRemove(server)
   }
}

This won't work, as this will cause a ConcurrentModificationException. I tried to make a copy of the list

List<ServerObject> copyList = new ArrayList<ServerObject>(this.servers);

and use that as the list for the foreach-loop. But then it might be possible that an other thread appends a Server to the servers list while I am iterating over copyList but closeCurrentlyOpen is supposed to result in an emtpy list. As the addServerToList method is synchronized to the servers-list, doing this

public void closeCurrentlyOpen() {
   synchronized(this.servers) {
     for(ServerObject server : this.servers) {
        stopAndRemove(server)
     }
    }
}

will solve the problem with modifications. But then I can not synchronize the code in the stopAndRemove method which is necessary if it is directly called.

I seems to me that the design of this three methods probably needs a workover. Ideas anybody?