Peptides that bind to major histocompatibility complex products (MHC) are known to exhibit certain sequence motifs which, though common, are neither necessary nor sufficient for binding: MHCs bind certain peptides that do not have the characteristic motifs and only about 30% of the peptides having the required motif, bind. In order to develop and test more accurate methods we measured the binding affinity of 463 nonamer peptides to HLA-A2.1. We describe two methods for predicting whether a given peptide will bind to an MHC and apply them to these peptides. One method is based on simulating a neural network and another, called the polynomial method, is based on statistical parameter estimation assuming independent binding of the side-chains of residues. We compare these methods with each other and with standard motif-based methods. The two methods are complementary, and both are superior to sequence motifs. The neural net is superior to simple motif searches in eliminating false positives. Its behavior can be coarsely tuned to the strength of binding desired and it is extendable in a straightforward fashion to other alleles. The polynomial method, on the other hand, has high sensitivity and is a superior method for eliminating false negatives. We discuss the validity of the independent binding assumption in such predictions.