In the long version of his Ph.D. thesis, Hugh Everett III developed pure wave mechanics as a way of solving the quantum measurement problem faced by the standard von Neumann-Dirac collapse formulation of quantum mechanics.1 Pure wave mechanics, however, encounters problems of its own. I will briefly review Everett’s description in his thesis of the standard measurement problem, how pure wave mechanics solves it, and the problems pure wave mechanics itself faces; then I will explain how one might nevertheless understand pure wave mechanics as a successful physical theory given the notion of faithfulness that Everett presents at the end of his long thesis. The result is a structural interpretation of pure wave mechanics as an empirically faithful theory. The standard collapse formulation of quantum mechanics has two dynamical laws: Process 1: The discontinuous change brought about by the observation of a quantity with eigenstates φ1, φ2,. . ., in which the state ψ will be changed to the state φj with probability |(ψ, φj)Ӛ. Process 2: The continuous, deterministic change of state of the (isolated) system with time according to a wave equation