Bitmap indexes are known to be efficient for ad-hoc range queries that are common in data warehousing and scientific applications. However, they suffer from the curse of cardinality, that is, their efficiency deteriorates as attribute cardinalities increase. A number of strategies have been proposed, but none of them addresses the problem adequately. In this paper, we propose a novel binned bitmap index that greatly reduces the cost to answer queries, and therefore breaks the curse of cardinality. The key idea is to augment the binned index with an Order-preserving Bin-based Clustering (OrBiC) structure. This data structure significantly reduces the I/O operations needed to resolve records that can not be resolved with the bitmaps. To further improve the proposed index structure, we also present a strategy to create single-valued bins for frequent values. This strategy reduces index sizes and improves query processing speed. Overall, the binned indexes with OrBiC great improves the query processing speed, and are 3 -- 25 times faster than the best available indexes for high-cardinality data.