We consider the class of Bayesian environments with independent types, and utility functions which are both quasi-linear in a private good and linear in a one-dimensional private-value type parameter. We call these "independent linear environments". For these environments, we fully characterize interim efficient allocation rules which satisfy interim incentive compatibility and interim individual rationality constraints. We also prove that they correspond to decision rules based on virtual surplus maximization, together with the appropriate incentive taxes. We demonstrate how these techniques can be applied easily to the design of auctions, markets, bargaining rules, public good provision, and assignment problems.