  The results and main steps of an analytic calculation of radiative-recoil
corrections of order $\alpha(Z\alpha)^5(m/M)m$ to the Lamb shift in hydrogen
are presented. The calculations are performed in the infrared safe Yennie
gauge. The discrepancy between two previous numerical calculations of these
corrections existing in the literature is resolved. Our new result eliminates
the largest source of the theoretical uncertainty in the magnitude of the
deuterium-hydrogen isotope shift.
