  We establish existence with sharp rates of decay and distance from the
Chapman--Enskog approximation of small-amplitude shock profiles of a class of
semilinear relaxation systems including discrete velocity models obtained from
Boltzmann and other kinetic equations. Our method of analysis is based on the
macro--micro decomposition introduced by Liu and Yu for the study of Boltzmann
profiles, but applied to the stationary rather than the time-evolutionary
equations. This yields a simple proof by contraction mapping in weighted $H^s$
spaces.
