SDDSs (Scalable Distributed Data Structures) are access methods specifically designed to satisfy the high performance requirements of a distributed computing environment made up by a collection of computers connected through a high speed network. In this paper we present and discuss performances of ADST, a new order preserving SDDS with a worst-case constant cost for exact-search queries, a worst-case logarithmic cost for update queries, and an optimal worst-case cost for range search queries of O(k) messages, where k is the number of servers covering the query range. Moreover, our structure has an amortized almost constant cost for any single-key query. Finally, our scheme can be easily generalized to manage k-dimensional points, while maintaining the same costs of the 1-dimensional case.