The Relaxed Complex method, an approach to structure-based drug design that incorporates the flexibilities of both the ligand and target protein, was applied to the immunodeficiency virus protease system. The control cases used AutoDock3.0.5 to dock a fully flexible version of the prospective drug JE-2147 (aka SM-319777 or KNI-764) to large ensembles of conformations extracted from conventional, all atom, explicitly solvated molecular dynamic simulations of the wild type, and the V82F/I84V drug-resistant mutant of HIV-1 protease. The best set of run parameters from the control cases produced robust results when used against 2200 different conformations of the wild-type HIV-1 protease or against 2200 conformations of the mutant. The results of the control cases, the published advice from experts, and structural intuition were used to design a new series of 23 potential active site inhibitors. The compounds were evaluated by docking them against 700 different conformations of the V82F/I84V mutant. The results of this first round of lead optimization were quite promising. Approximately one-third of that series performed at least slightly better than the parent compound, and four of those compounds displayed significantly better binding affinities against that drug-resistant mutant (within our computational model).