Simplified models of the protein-folding process have led to valuable insights into the generic properties of the folding of heteropolymers. On the basis of theoretical arguments, Shakhnovich and Gutin [(1993) Proc. Natl. Acad. Sci. USA 90, 7195-7199] have proposed a specific method to generate folding sequences for one of these. Here we present a model of folding in heteropolymers that is comparable in simplicity but different in spirit to the one studied by Shakhnovich and Gutin. In our model, the proposed recipe for constructing folding sequence fails. We find that, as a rule, the construction of folding sequences is impossible to achieve by looking at the native conformation only. Rather, competing conformations have to be taken into account too. An evolutionary algorithm that generates folding sequences by optimizing both stability of the native state and folding time is described. Remarkably, this algorithm produces, among others, sequences that fold reproducibly to metastable states.