Phylogenetic footprinting is a comparative genomics approach for predicting transcription factor binding sites, where a set of orthologous regulatory regions are compared and short conserved regions are identified as putative binding sites. Two main families of approaches exist: alignment-based and motif-based approaches. Each of the two approaches has advantages and disadvantages. Here, we present a new approach for phylogenetic footprinting that combines the strengths of the two approaches. Our method uses alignment information where it is available and reliable, but also allows to find binding sites in regions that are overall too poorly conserved to be aligned. We introduce a new algorithmic problem, the Alignment-Compatible Substring Parsimony Problem, where we ask to identify short substrings that are phylogenetically conserved and whose positions in their respective sequences are compatible with the partial ordering defined by a set of local alignments. We describe how this prob...