Most combinatorial libraries are 'sparse' in that only a tiny fraction of the relevant class of compounds is represented. This sparseness can be compensated in some measure by alternating rounds of selection with rounds of mutagenesis. Thus, clones are selected from the initial library by some criterion of 'fitness', such as affinity for a particular receptor. The selected clones are then mutagenized to generate a mutant library, which serves as input to the next round of selection, and so on. If the first round of selection is too stringent, rejecting all but the very fittest clone in the initial library (the 'initial champion'), we might miss 'dark horses': clones in the initial library that are inferior to the initial champion, yet can be mutated to even higher fitness than can that champion. A more thoughtful strategy is to alternate nonstringent selection with simultaneous mutagenesis of many selected-clones en masse.