  The first in m/M and fourth in Z\alpha (pure recoil) correction to a hydrogen
energy level is found. This correction comprises two contributions, one coming
from the atomic scale, the other from distances of the Compton wavelength
order. Two different perturbation schemes are used to calculate the former. One
of them exploits as unperturbed the solution to the Dirac-Coulomb problem, the
nucleus' slow motion being the source of the perturbation. The alternative
scheme treats both the electron and the nucleus as slow, while relativistic
effects are considered perturbatively. The short-distance contribution is found
in the Feynman and Coulomb gauges. Recent results for P levels are confirmed,
in contrast with those for S levels. Numerically, the shift equals 2.77 kHz for
the ground state and 0.51 kHz for 2S state.
