Background: While most multiple sequence alignment programs expect that all or most of their input is known to be homologous, and penalise insertions and deletions, this is not a reasonable assumption for non-coding DNA, which is much less strongly conserved than protein-coding genes. Arguing that the goal of sequence alignment should be the detection of homology and not similarity, we incorporate an evolutionary model into a previously published multiple sequence alignment program for non-coding DNA, Sigma, as a sensitive likelihood-based way to assess the significance of alignments. Version 1 of Sigma was successful in eliminating spurious alignments but exhibited relatively poor sensitivity on synthetic data. Sigma 1 used a p-value (the probability under the "null hypothesis" of non-homology) to assess the significance of alignments, and, optionally, a background model that captured short-range genomic correlations. Sigma version 2, described here, retains these features,...