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Bitmap indices are efficient for answering queries on low-cardinality attributes. In this article, we present a new compression scheme called Word-Aligned Hybrid (WAH) code that makes compressed bitmap indices efficient even for high-cardinality attributes. We further prove that the new compressed bitmap index, like the best variants of the B-tree index, is optimal for one-dimensional range queries. More specifically, the time required to answer a one-dimensional range query is a linear function of the number of hits. This strongly supports the well-known observation that compressed bitmap indices are efficient for multidimensional range queries because results of one-dimensional range queries computed with bitmap indices can be easily combined to answer multidimensional range queries. Our timing measurements on range queries not only confirm the linear relationship between the query response time and the number of hits, but also demonstrate that WAH compressed indices answer queries faster than the commonly used indices including projection indices, B-tree indices, and other compressed bitmap indices.