Improving the accuracy and efficiency of motif recognition is an important computational challenge that has application to detecting transcription factor binding sites in genomic data. Closely related to motif recognition is the CONSENSUS STRING decision problem that asks, given a parameter d and a set of l-length strings S = {s1, ..., sn}, whether there exists a consensus string that has Hamming distance at most d from any string in S. A set of strings S is pairwise bounded if the Hamming distance between any pair of strings in S is at most 2d. It is trivial to determine whether a set is pairwise bounded, and a set cannot have a consensus string unless it is pairwise bounded. We use CONSENSUS STRING to determine whether or not a pairwise bounded set has a consensus. Unfortunately, CONSENSUS STRING is NP-complete. The lack of an efficient method to solve the CONSENSUS STRING problem has caused it to become a computational bottleneck in MCL-WMR, a motif recognition program capable of solving difficult motif recognition problem instances.