The fewer threads you have, the smaller state they share, and the simpler their interaction pattern on this shared state, the simpler your life will be.
You say Lists are throwing ConcurrentModificationException. I take it that your lists are acessed by seperate threads. So the first thing you should ask yourself is whether this is necessary. Is it not possible for the second thread to operate on a copy of the list?
If it is indeed necessary for the threads to access the list concurrently, locking the list during the entire traversal might be an option (Iterators are invalidated if the list is modified by any other means than that iterator). Of course, if you do other things while traversing the list, this traversal might take long, and locking out other threads might threaten the liveness of the system.
Also keep in mind that if the list is shared state, so are its contents, so if you intend to circumwent locking by copying the list, be sure to perform a deep copy, or prove that the objects contained in the list are themselves thread safe.
