sort concurrent map entries by value

Is there any way to create a thread-safe implementation of Map that maintains it's entries sorted by value? I know I can create a thread-safe Map like this

ConcurrentMap rankings = new ConcurrentHashMap();

And I can then get the entries sorted by value by passing it to a utility method like this:

public static > Map sortByValue(Map map) {
    List> list = new LinkedList>(map.entrySet());
    Collections.sort(list, new Comparator>() {
        @Override
        public int compare(Map.Entry o1, Map.Entry o2) {
            return (o1.getValue()).compareTo(o2.getValue());
        }
    });

    Map result = new LinkedHashMap();
    for (Map.Entry entry : list) {
        result.put(entry.getKey(), entry.getValue());
    }
    return result;
}

But what I'm looking for is a thread-safe Map that maintains the entries sorted by value, so that I don't have to call a method such as the above after every insertion/removal in order to keep the entries sorted by value. I guess I'm looking for an implementation that combines the behavior of ConcurrentHashMap and LinkedHashMap, but haven't found one yet.

ConcurrentSkipListMap almost provides what I want, but it only seems to support sorting by key value.