Multiplicity of equilibria and the dependence on strong common knowledge assumptions are well-known problems in mechanism design. We address them by studying full implementation via transfer schemes, under general restrictions on agents' beliefs. We show that incentive-compatible transfers ensure uniqueness—and hence full implementation—if they induce sufficiently weak strategic externalities. We then design transfers for full implementation by using information on beliefs in order to weaken the strategic externalities of the baseline canonical transfers. Our results rely on minimal restrictions on agents' beliefs, specifically on moments of the distribution of types, that arise naturally in applications.