The starting point for any alignment of mammalian genomes is the computation of exact matches satisfying various criteria. Time-efficient, O(n), data structures for this computation, such as the suffix tree, require O(n log(n)) space, several times the space of the genomes themselves. Thus, any reasonable whole-genome comparative project finds itself requiring tens of Gigabytes of RAM to maintain time-efficiency. This is beyond most modern workstations. With a new data structure, the compressed suffix array (CSA) implemented via the Burrows-Wheeler transform, we can trade time-efficiency for space-efficiency, taking O(n log(n)) time, but running in O(n) space, typically in total space less than or equal to that of the genomes themselves. If space is more expensive than time, this is an appropriate approach to consider. The most space-efficient implementation of this data structure requires 5 bits per nucleotide character to build on-line, in the worst case, and 2.5 bits per character to store once built. We present a description of this data structure and how it is used to obtain matches. An implementation (called bbbwt) is demonstrated by aligning two mammalian genomes on a modest workstation equipped with under 2 GB of free RAM in time superior to that of the implementations of other data structures.