A method is described for performing global alignment of noncoding DNA sequences based on an evolutionary model parameterized by the frequency distribution of lengths of insertion/deletion events (indels) and their rate relative to nucleotide substitutions. A stochastic hill-climbing algorithm is used to search for the most probable alignment between a pair of sequences or three sequences of known phylogenetic relationship. The performance of the procedure, parameterized according to the empirical distribution of indel lengths in noncoding DNA of Drosophila species, is investigated by simulation. We show that there is excellent agreement between true and estimated alignments over a wide range of sequence divergences, and that the method outperforms other available alignment methods.