  We study the effect of returning radiation on the shape of the X-ray
reflection spectrum in the case of thin accretion disks. We show that the
returning radiation mainly influences the observed reflection spectrum for a
large black hole spin (a > 0.9) and a compact primary source of radiation close
to the black hole at height h < 5 $r_\mathrm{g}$, and that it dominates the
reflected flux for extreme values of spin and compactness. The main effect of
the returning radiation is to increase the irradiating flux on to the outer
parts of the accretion disk, leading to stronger reflection and a flatter
overall emissivity profile. By analyzing simulated observations we show that
neglecting returning radiation in existing studies of reflection dominated
sources has likely resulted in overestimating the height of the corona above
the black hole. An updated version of the publicly available relxill suite of
relativistic reflection models which includes returning radiation is also
presented.
