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Data warehouses contain data consolidated from several operational databases and provide the historical, and summarized data which is more appropriate for analysis than detail, individual records. Fast response time is essential for on-line decision support. A bitmap index could reach this goal in read-mostly environments. For the data with high cardinality in data warehouses, a bitmap index consists of a lot of bitmap vectors, and the size of the bitmap index could be much larger than the capacity of the disk. The WAH strategy has been presented to solve the storage overhead. However, when the bit density and clustering factor of 1's increase, the bit strings of the WAH strategy become less compressible. Therefore, in this paper, we propose the FZ strategy which compresses each bitmap vector to reduce the size of the storage space and provide efficient bitwise operations without decompressing these bitmap vectors. From our performance simulation, the FZ strategy could reduce the storage space more than the WAH strategy.