Kinetic data on a number of protein-protein associations have provided evidence for the initial formation of a pre-equilibrium encounter complex that subsequently relaxes to the final stereospecific complex. Site-directed mutagenesis and brownian dynamics simulations have suggested that the rate of association can be modulated by perturbations in charge distribution outside the direct interaction surfaces. Furthermore, rate enhancement through non-specific binding may occur by either a reduction in dimensionality or the presence of a short-range, non-specific attractive potential. Here, using paramagnetic relaxation enhancement, we directly demonstrate the existence and visualize the distribution of an ensemble of transient, non-specific encounter complexes under equilibrium conditions for a relatively weak protein-protein complex between the amino-terminal domain of enzyme I and the phosphocarrier protein HPr. Neither the stereospecific complex alone nor any single alternative conformation can account fully for the intermolecular paramagnetic relaxation enhancement data. Restrained rigid-body simulated annealing refinement against the paramagnetic relaxation enhancement data enables us to obtain an atomic probability distribution map of the non-specific encounter complex ensemble that qualitatively correlates with the electrostatic surface potentials on the interacting proteins. Qualitatively similar results are presented for two other protein-protein complexes.