The lifetime distribution for initially monoenergetic photons subject to relativ-istic Compton (Klein-Nishina) scattering is evaluated using an analog of neutron slowing-down theory. By using reasonable approximations to the energy dependence of photon cross sections, this distribution and the lifetime-averaged cross sections are evaluated in closed form. The averaged cross sections are useful when all once-or-more scattered photons from a given source energy must be treated as a single group.