We consider dictionaries over the universe U = {0, 1}w on a unit-cost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n)O(1) and updates in time (log n)O(1) , where n is the size of the set stored. This is the first such data structure to simultaneously achieve query time (log n)o(1) and update time O(2(log n)c ) for a constant