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We generalize the familiar position-specific score matrix (PSSM), aka weight matrix, by considering a log-odds score for (nonadjacent) k-tuple frequencies, each k-tuple score weighted by the product of its mutual information and its statistical significance, as measured by a point estimator for the p-value of the mutual information. Performance of this new approach, along with other variants of generalized PSSM and profile methods, is measured by receiver-operating characteristic (ROC) curves for the specific problem of signal peptide cleavage site recognition. We additionally compare Vert's recent support vector machine string kernel, Brown's joint probability approximation algorithm and the method WAM. Similar algorithm comparisons are made, though not as extensively, in the case of disulfide bond recognition. While in the case of signal peptide cleavage site recognition, the monoresidue PSSM is essentially competitive, within the limits of statistical significance, even against Vert's support vector machine kernel, diresidue and triresidue PSSM methods display improved performance over monoresidue PSSM for disulfide bond recognition.