Bit arrays, or bitmaps, are used to significantly speed up set operations in several areas, such as data warehousing, information retrieval, and data mining, to cite a few. However, bitmaps usually use a large storage space, thus requiring compression. Nevertheless, there is a space-time tradeoff among compression schemes. The Word Aligned Hybrid (WAH) bitmap compression trades some space to allow for bitwise operations without first decompressing bitmaps. WAH has been recognized as the most efficient scheme in terms of computation time. In this paper we present CONCISE (Compressed 'n' Composable Integer Set), a new scheme that enjoys significatively better performances than those of WAH. In particular, when compared to WAH, our algorithm is able to reduce the required memory up to 50%, by having similar or better performance in terms of computation time. Further, we show that CONCISE can be efficiently used to manipulate bitmaps representing sets of integral numbers in lieu of well-known data structures such as arrays, lists, hashtables, and self-balancing binary search trees. Extensive experiments over synthetic data show the effectiveness of our approach.