Brandenburger and Dekel have shown that common belief of rationality (CBR) characterizes rationalizable strategies, which are also characterized by a refinement of subjective correlated equi- librium called a posteriori equilibrium. It is possible that players’ beliefs are incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require players’ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. Aumann has shown that, under the common prior assumption (CPA), common belief of rationality characterizes strategies in the support of an objective correlated equilibrium. Under the CPA, without loss of generality, all players’ beliefs can be assumed to be conservative. We consider the consequences of common convervative belief of rationality (CCBR), without the common prior assumption. We show that CCBR characterizes strategies in the support of a subjective correlated equilibrium where all players’ beliefs have common support. We also define a notion of strong rationalizability, and show that this is characterized by CCBR.