We present a rapidly executable minimal binding energy model for molecular docking and use it to explore the energy landscape in the vicinity of the binding sites of four different enzyme inhibitor complexes. The structures of the complexes are calculated starting with the crystal structures of the free monomers, using DOCK 4.0 to generate a large number of potential configurations, and screening with the binding energy target function. In order to investigate possible correlations between energy and variation from the native structure, we introduce a new measure of similarity, which removes many of the difficulties associated with root mean square deviation. The analysis uncovers energy gradients, or funnels, near the binding site, with decreasing energy as the degree of similarity between the native and docked structures increases. Such energy funnels can increase the number of random collisions that may evolve into productive stable complex, and indicate that short-range interactions in the precomplexes can contribute to the association rate. The finding could provide an explanation for the relatively rapid association rates that are observed even in the absence of long-range electrostatic steering.