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We present "Pipe 'n Prune" (PnP), a new hybrid method for iceberg-cube query computation. The novelty of our method is that it achieves a tight integration of top-down piping for data aggregation with bottom-up a priori data pruning. A particular strength of PnP is that it is very efficient for all of the following scenarios: (1) Sequential iceberg-cube queries. (2) External memory iceberg-cube queries. (3) Parallel iceberg-cube queries on shared-nothing PC clusters with multiple disks.