The Optical Mapping System constructs ordered restriction maps spanning entire genomes through the assembly and analysis of large datasets comprising individually analyzed genomic DNA molecules. Such restriction maps uniquely reveal mammalian genome structure and variation, but also raise computational and statistical questions beyond those that have been solved in the analysis of smaller, microbial genomes. We address the problem of how to filter maps that align poorly to a reference genome. We obtain map-specific thresholds that control errors and improve iterative assembly. We also show how an optimal self-alignment score provides an accurate approximation to the probability of alignment, which is useful in applications seeking to identify structural genomic abnormalities.