SummaryCompressed bitmap indexes are used in databases and search engines. Many bitmap compression techniques have been proposed, almost all relying primarily on run‐length encoding (RLE). However, on unsorted data, we can get superior performance with a hybrid compression technique that uses both uncompressed bitmaps and packed arrays inside a two‐level tree. An instance of this technique, Roaring, has recently been proposed. Due to its good performance, it has been adopted by several production platforms (e.g., Apache Lucene, Apache Spark, Apache Kylin, and Druid). Yet there are cases where run‐length‐encoded bitmaps are smaller than the original Roaring bitmaps—typically when the data are sorted so that the bitmaps contain long compressible runs. To better handle these cases, we build a new Roaring hybrid that combines uncompressed bitmaps, packed arrays, and RLE‐compressed segments. The result is a new Roaring format that compresses better. Overall, our new implementation of Roaring can be several times faster (up to two orders of magnitude) than the implementations of traditional RLE‐based alternatives (WAH, Concise, and EWAH) while compressing better. We review the design choices and optimizations that make these good results possible. Copyright © 2016 John Wiley & Sons, Ltd.