  Elaborating on a previous letter, we use a new approach to compute energy
levels of a non-relativistic bound-state of two constituents, with masses m and
M, by systematic expansions - one in powers of m/M and another in powers of
(1-m/M). Technical aspects of the calculations are described in detail.
Theoretical predictions are given for O(alpha(Z*alpha)^5) radiative recoil and
O((Z*alpha)^6) pure recoil corrections to the average energy shift and
hyperfine splitting relevant for hydrogen, muonic hydrogen, and muonium.
