Data cubes facilitate fast On-Line Analytical Processing (OLAP). Iceberg cubes are special cubes comprise only the multidimensional groups satisfying some user-specified constraints. Previous algorithms have focused on iceberg cubes defined by relatively simple constraints such as “COUNT(*) ≥ δ” and “COUNT(*) ≥ δ AND AV G(Profit) ≥ α”. We propose an algorithm I-Cubing that computes iceberg cubes defined by complex constraints involving multiple predicates of aggregates such as “COUNT(*) ≥ δ AND (AV G(Profit) ≥ α OR AV G(profit) ≤ β)”. State-of-the-art iceberg cubing algorithms: BUC cannot handle such cases whereas H-Cubing has to incur extra cost. Our proposed bounding technique can prune for all the given constraints at once without extra cost. Experiments show that bounding has superior pruning power and I-Cubing is twice as fast as H-Cubing. Furthermore, I-Cubing performs equally well with more complex constraints.