  We consider the Comptonisation of the photons that make up the
relativistically blurred reflection that is commonly detected from the
accretion discs of AGN by the coronae of energetic particles believed to give
rise to the powerful X-ray continua by the inverse-Compton scattering of
thermal seed photons from the disc. Recent measurements of the emissivity
profiles of accretion discs as well as reverberation time lags between the
primary X-ray continuum and the reflection suggest that this corona is situated
at a low height above the disc and extends radially, tens of gravitational
radii over the disc surface, hence should also Compton scatter the reflected
X-rays. We find that the detection of blurred reflection from as close in as
the innermost stable circular orbits (ISCOs) of maximally rotating black holes
is consistent with such coronae, but requires that the corona be patchy,
consisting perhaps of a number of isolated flares throughout the region.
Considering only the requirement that it be possible to detect reflection from
the ISCO, we find that at any given moment, the covering fraction of the inner
part of the accretion disc by the corona needs to be less than 85 per cent,
though allowing for the detection of 'reflection-dominated' spectra in which
the total reflected flux exceeds that seen in the continuum requires covering
fractions as low as 50 or 25 per cent.
