Opponents of would-be proliferators would like to leverage the threat of preventive war to convince would-be proliferators not to develop nuclear weapons without having to offer any concessions. How do negotiations play out when the would-be proliferators doubt the credibility of such threats? This chapter develops a model of uncertainty over a declining state's cost of preventive war. Weak declining states sometimes offer full concessions and sometimes bluff strength by offering no concessions. As a result, upon not receiving concessions, potential proliferators do not know whether they should develop a weapon. They optimally respond by sometimes challenging the bluff, which results in nuclear proliferation against weak opponents and preventive war against strong opponents. I then trace the mechanism by studying Israel's response to Iraq's nuclear program.