The increasing latency between memory and processor speeds has made it imperative for algorithms to reduce expensive accesses to main memory. In earlier work, we presented cache-conscious algorithms for sorting strings, that have been shown to be almost two times faster than the previous algorithms, mainly due to better usage of the cache. In this paper, we propose two new algorithms, Burstsort and MEBurstsort, for sorting large sets of integer keys. Our algorithms use a novel approach for sorting integers, by dynamically constructing a compact trie which is used to allocate the keys to containers. These keys are then sorted within the cache. The new algorithms are simple, fast and efficient. We compare them against the best existing algorithms using several collections and data sizes. Our results show that MEBurstsort is up to 3.5 times faster than memory-tuned quicksort for 64-bit keys and up to 2.5 times faster for 32-bit keys. For 32-bit keys, on 10 of the 11 collections used, MEBurstsort was the fastest, whereas for 64-bit keys, it was the fastest for all collections.