Recently, novel technologies for isolation of nucleic acid molecules with specific biological activities have been reported. In each case, the enrichment process involves repeated rounds of selection from complex mixtures of nucleic acid sequences, followed by polymerase chain reaction (PCR) amplification of ligand sequences that function in the desired manner. Particular variations in experimental conditions can dramatically alter the outcome of these processes. In this study, we use mathematical analysis and computer simulation to predict which variations have the greatest impact and to develop strategies and guidelines for enhanced effectiveness. First, we perform reconstruction tests to demonstrate that a mathematical description based on equilibrium binding is sufficient to explain the high levels of enrichment attained in the laboratory after just a few rounds. Then, we show the expected enrichment for an extensive range of conditions; and, finally, we determine the optimum protein and nucleic acid concentrations to use for maximum enrichment, while also ensuring a high likelihood of recovering even the rare molecule that binds well. The strategies and guidelines for enhanced effectiveness are generally applicable to processes for systematic enrichment of DNA, RNA or peptide ligands and have been implemented in an interactive simulation program for integrated non-linear optimization of enrichment using any target of interest. © 1991.