A fully covariant two-body equation is applied to the theory of hydrogen, muonium, and positronium spectra. Both particles are treated fully relativistically and complete spin algebras for both particles are taken into account. The major part of the 16 × 16 wave equation is exactly soluble including recoil of both particles to all orders. The terms of order α 5, α 5 are treated perturbatively (although the equation is in principle numerically solvable to all orders). Self-energy (loop) effects are partly considered by an (effective) anomalous magnetic moment, but in a dynamical way using a Pauli coupling from the beginning. The theory simplifies and improves the bound-state QED problems in a number of ways.