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We present a new algorithm for deterministic sorting on the Bulk-Synchronous Parallel (BSP) model of computation. We sort n keys using a partitioning scheme that achieves the requirements of efficiency (one-optimality) and insensitivity against initial key distribution. Although we employ sampling to realize efficiency, we give a precise worst-case estimation of the maximum imbalance which might occur. The algorithm is one-optimal for a wide range of the BSP parameters in the sense that its speedup on p processors is asymptotically (1 -o(l))p. Keywords: BSP model -algorithms -sorting -deterministic sampling The BSP ModelThe Bulk-Synchronous Parallel (BSP) model of computation has been proposed [24,25] as a unified framework for the design, analysis and programming of general purpose parallel computing systems.