We describe here the use of a rapid computational method to predict the relative binding strengths of a series of small-molecule ligands for the serine proteinase trypsin. Flexible molecular models of the ligands were docked to the proteinase using an all-atom potential set, without cutoff limits for the non-bonded and electrostatic energies. The binding-strength calculation is done directly in terms of a molecular mechanics potential. The binding of eighteen different compounds, including non-binding controls, has been successfully predicted. The measured Ki is correlated with the predicted energy. The correctness of the theoretical calculations is demonstrated with both kinetics measurements and X-ray structure determination of six enzyme-inhibitor complexes.