We show that efficient anonymous incentive compatible (dominant strategy) mechanisms for public goods eliminate externalities, i.e., each individual is unable to change the welfare of anyone else. The characterization is used to derive existence and non-existence results for models with a finite number of individuals and to explain existence results in the continuum. A similar characterization and conclusions are demonstrated for private goods in . However, unlike private goods, elimination of externalities with public goods implies that individuals cannot change the outcome. Hence, such mechanisms provide only weak incentives for truth-telling.