Molecular docking remains an important tool for structure-based screening to find new ligands and chemical probes. As docking ambitions grow to include new scoring function terms, and to address ever more targets, the reliability and extendability of the orientation sampling, and the throughput of the method, become pressing. Here we explore sampling techniques that eliminate stochastic behavior in DOCK3.6, allowing us to optimize the method for regularly variable sampling of orientations. This also enabled a focused effort to optimize the code for efficiency, with a three-fold increase in the speed of the program. This, in turn, facilitated extensive testing of the method on the 102 targets, 22,805 ligands and 1,411,214 decoys of the Directory of Useful Decoys-Enhanced (DUD-E) benchmarking set, at multiple levels of sampling. Encouragingly, we observe that as sampling increases from 50 to 500 to 2000 to 5000 to 20,000 molecular orientations in the binding site (and so from about 1×10(10) to 4×10(10) to 1×10(11) to 2×10(11) to 5×10(11) mean atoms scored per target, since multiple conformations are sampled per orientation), the enrichment of ligands over decoys monotonically increases for most DUD-E targets. Meanwhile, including internal electrostatics in the evaluation ligand conformational energies, and restricting aromatic hydroxyls to low energy rotamers, further improved enrichment values. Several of the strategies used here to improve the efficiency of the code are broadly applicable in the field.