  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 $q\sim 4-5$ (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.
