X-ray reflection off the accretion disc surrounding a black hole, together with the associated broad iron K$alpha$ line, has been widely used to constrain the innermost accretion-flow geometry and black hole spin. Some recent measurements have revealed steep reflection emissivity profiles in a number of active galactic nuclei and X-ray binaries. We explore the physically motivated conditions that give rise to the observed steep disc-reflection emissivity profiles. We perform a set of simulations based on the configuration of a possible future high-resolution X-ray mission. Computations are carried out for typical X-ray bright Seyfert-1 galaxies. We find that steep emissivity profiles with $qsim 4-5$ (where the emissivity is $epsilon (r) propto r^{-q}$) are produced considering either i) a lamp-post scenario where a primary compact X-ray source is located close to the black hole, or ii) the radial dependence of the disc ionisation state. We also highlight the role of the reflection angular emissivity: the radial emissivity index $q$ is overestimated when the standard limb-darkening law is used to describe the data. Very steep emissivity profiles with $q geq 7$ are naturally obtained by applying reflection models that take into account radial profile $xi (r)$ of the disc ionisation induced by a compact X-ray source located close to the central black hole.
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