  We have developed improved spectral models of relativistic reflection in the
lamppost and disc-corona geometries. The models calculate photon transfer in
the Kerr metric and give the observed photon-energy spectra produced by either
thermal Comptonization or an e-folded power law incident on a cold ionized
disc. Radiative processes in the primary X-ray source and in the disc are
described with the currently most precise available models. Our implementation
of the lamppost geometry takes into account the presence of primary sources on
both sides of the disc, which is important when the disc is truncated. We
thoroughly discuss the differences between our models and the previous ones.
