In this paper we show how a slight modification of (a, 2b)-trees allows us to perform member and neighbor queries in O(log n) time and updates in O(1) worst-case time (once the position of the inserted or deleted key is known). Our data structure is quite natural and much simpler than previous worst-case optimal solutions. It is based on two techniques : 1) bucketing, i.e., storing an ordered list of 2 log n keys in each leaf of an (a, 2b) tree, and 2) preventive splitting, i.e., splitting

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... before they can grow bigger than allowed. If only insertions are allowed, it can also be used as a finger search tree with O(log * n) worst-case update time.