One way to make more spectrum available is through white space sharing, where secondary spectrum users are allowed to transmit from any location except inside exclusion zones (EZs) that are drawn around primary spectrum users (PUs). However, EZ boundaries reveal the locations of PUs, and for some devices, location privacy is extremely important. Location privacy can be improved by increasing the area blocked inside EZs, but this decreases spectrum utilization efficiency. This paper derives a Pareto optimal strategy that builds on two such approaches: generating dummy PUs and creating EZs around them, and making EZs larger than needed for interference protection alone. We find that in many circumstances, including cases where an attacker threatens a jamming attack, the optimal strategy is to maximize the number of dummy PUs while making EZs as small as possible. In the remaining circumstances, the optimal strategy is to generate no dummy EZs. We derive the Pareto optimal results achieved by using whichever of these strategies is best for given circumstances, and show that the results are far superior to those achieved with some previously proposed algorithms. Moreover, with our approach, even a small increase in the amount of area blocked from secondary use can greatly improve location privacy for PUs, although as more and more area is blocked, there are diminishing returns.