  Recent interferometric surveys of nearby main-sequence stars show a faint but
significant near-infrared excess in roughly two dozen systems, i.$\,$e. around
$10\,\%$ to $30\,\%$ of stars surveyed. This excess is attributed to dust
located in the immediate vicinity of the star, the origin of which is highly
debated. We used previously published interferometric observations to constrain
the properties and distribution of this hot dust. Considering both scattered
radiation and thermal reemission, we modelled the observed excess in nine of
these systems. We find that grains have to be sufficiently absorbing to be
consistent with the observed excess, while dielectric grains with pure silicate
compositions fail to reproduce the observations. The dust should be located
within $\sim\,0.01-1\,au$ from the star depending on its luminosity.
Furthermore, we find a significant trend for the disc radius to increase with
the stellar luminosity. The dust grains are determined to be below
$0.2-0.5\,\mu\textrm{m}$, but above $0.02-0.15\,\mu\textrm{m}$ in radius. The
dust masses amount to $(0.2-3.5)\times10^{-9}\,M_\oplus$. The near-infrared
excess is probably dominated by thermal reemission, though a contribution of
scattered light up to $35\,\%$ cannot be completely excluded. The polarisation
degree predicted by our models is always below $5\,\%$, and for grains smaller
than $\sim0.2\,\mu\textrm{m}$ even below $1\,\%$. We also modelled the observed
near-infrared excess of another ten systems with poorer data in the
mid-infrared. The basic results for these systems appear qualitatively similar,
yet the constraints on the dust location and the grain sizes are weaker.
