This is an investigation of methods for finding short motifs that only occur in a fraction of the input sequences. Unlike local search techniques that may not reach a global optimum, the method proposed here is guaranteed to produce the motifs with greatest z-scores. This method is illustrated for the Ribosome Binding Site Problem, which is to identify the short mRNA 50 untranslated sequence that is recognized by the ribosome during initiation of protein synthesis. Experiments were performed to solve this problem for each of fourteen sequenced prokaryotes, by applying the method to the full complement of genes from each. One of the interesting results of this experimentation is evidence that the recognized sequence of the thermophilic archaea A. fulgidus, M. jannaschii, M. thermoautotrophicum,and P. horikoshii may be somewhat different than the well known Shine-Dalgarno sequence.