Ongoing changes in computer performance are affecting the efficiency of string sorting algorithms. The size of main memory in typical computers continues to grow, but memory accesses require increasing numbers of instruction cycles, which is a problem for the most efficient of the existing string-sorting algorithms as they do not utilise cache particularly well for large data sets. We propose a new sorting algorithm for strings, burstsort, based on dynamic construction of a compact trie in which strings are kept in buckets. It is simple, fast, and efficient. We experimentally compare burstsort to existing string-sorting algorithms on large and small sets of strings with a range of characteristics. These experiments show that, for large sets of strings, burstsort is almost twice as fast as any previous algorithm, due primarily to a lower rate of cache miss.