Strand-seq is a single-cell sequencing technique to finely map sister chromatid exchanges (SCEs) and other rearrangements. To analyze these data, we introduce BAIT, software which assigns templates and identifies and localizes SCEs. We demonstrate BAIT can refine completed reference assemblies, identifying approximately 21 Mb of incorrectly oriented fragments and placing over half (2.6 Mb) of the orphan fragments in mm10/GRCm38. BAIT also stratifies scaffold-stage assemblies, potentially accelerating the assembling and finishing of reference genomes. BAIT is available at http://sourceforge.net/projects/bait/.