Administrators/Decision Makers (DMs) responsible for making locational decisions for public facilities have many other overriding factors to consider that dominate traditional OR/MS objectives that relate to response time. We propose that an appropriate role for the OR/MS analyst is to help the DMs identify a good set of solutions rather than an optimal solution that may not be practical. In this paper, good solutions can be generated/prescribed assuming that the DMs have (i) a dispersion criterion that ensures a minimum distance between every pair of facilities, and (ii) a population criterion which stipulates that the distance from a demand point to its closest facility is inversely proportional to its population, and (iii) an equity criterion which stipulates that no demand point is further than a specified distance from its closest facility. We define parameters capturing these three criteria and specify values for them based on the p-median solution. Sensitivity analysis with respect to the parameters is performed and computational results for both real and simulated networks are reported. Our results show close collaboration with the p-median solution when decision makers restrict location to demand points, and use parameter values for the population, dispersion, and equity criteria as implied by the p-median solution. The significance of our work is twofold. For practitioners, it is comforting to know that using common-sense measures such as the above criteria result in fairly good solutions. For researchers it suggests the need for developing techniques for finding the k best solutions of the p-median problem.