Bitmap indices are efficient data structures for querying read-only data with low attribute cardinalities. To improve the efficiency of the bitmap indices on attributes with high cardinalities, we present a new strategy to evaluate queries using bitmap indices. This work is motivated by a number of scientific data analysis applications where most attributes have cardinalities in the millions. On these attributes, binning is a common strategy to reduce the size of the bitmap index. In this article we analyze how binning affects the number of pages accessed during query processing, and propose an optimal way of using the bitmap indices to reduce the number of pages accessed. Compared with two basic strategies the new algorithm reduces the query response time by up to a factor of two. On a set of 5-dimensional queries on real application data, the bitmap indices are on average 10 times faster than the projection index.