Privacy and trust affect our strategic thinking, yet they have not been precisely modeled in mechanism design. In settings of incomplete information, traditional implementations of a normal-form mechanism -- by disregarding the players' privacy, or assuming trust in a mediator -- may not be realistic and fail to reach the mechanism's objectives. We thus investigate implementations of a new type. We put forward the notion of a perfect implementation of a normal-form mechanism M: in essence, an extensive-form mechanism exactly preserving all strategic properties of M, without relying on a trusted party or violating the privacy of the players. We prove that any normal-form mechanism can be perfectly implemented via envelopes and an envelope-randomizing device (i.e., the same tools used for running fair lotteries or tallying secret votes).