  We describe a new approach to computing energy levels of a non-relativistic
bound-state of two constituents with masses M and m, by a systematic expansion
in powers of m/M. After discussing the method, we demonstrate its potential
with an example of the radiative recoil corrections to the Lamb shift and
hyperfine splitting relevant for the hydrogen, muonic hydrogen, and muonium. A
discrepancy between two previous calculations of O(alpha(Zalpha)^5 m^2/M)
radiative recoil corrections to the Lamb shift is resolved and several new
terms of O(alpha(Zalpha)^5 m^4/M^3) and higher are obtained.
