We describe an algorithm to predict tertiary structures of small proteins. In contrast to most current folding algorithms, it uses very few energy parameters. Given the secondary structural elements in the sequence--alpha-helices and beta-strands--the algorithm searches the remaining conformational space of a simplified real-space representation of chains to find a minimum energy of an exceedingly simple potential function. The potential is based only on a single type of favorable interaction between hydrophobic residues, an unfavorable excluded volume term of spatial overlaps and, for sheet proteins, an interstrand hydrogen bond interaction. Where appropriate, the known disulfide bonds are constrained by a square-law potential. Conformations are searched by a genetic algorithm. The model predicts reasonably well the known tertiary folds of seven out of the 10 small proteins we consider. We draw two conclusions. First, for the proteins we tested, this exceedingly simple potential function is no worse than others having hundreds of energy parameters in finding the right general tertiary structures. Second, despite its simplicity, the potential function is not the weak link in this algorithm. Differences between our predicted structures and the correct targets can be ascribed to shortcomings in our search strategy. This potential function may be useful for testing other conformational search strategies.