  The vertical thickness of debris discs is often used as a measure of these
systems' dynamical excitation and as clues to the presence of hidden massive
perturbers such as planetary embryos. However, this argument could be flawed
because the observed dust should be naturally placed on inclined orbits by the
combined effect of radiation pressure and mutual collisions. We critically
reinvestigate this issue and numerically estimate what the "natural" vertical
thickness of a collisionally evolving disc is, in the absence of any additional
perturbing body. We use a deterministic collisional code, following the
dynamical evolution of a population of indestructible test grains suffering
mutual inelastic impacts. Grain differential sizes as well as the effect of
radiation pressure are taken into account. We find that, under the coupled
effect of radiation pressure and collisions, grains naturally acquire
inclinations of a few degrees. The disc is stratified with respect to grain
sizes, with the smallest grains having the largest vertical dispersion and the
bigger ones clustered closer to the midplane. Debris discs should have a
minimum "natural" observed aspect ratio $h_{min}\sim 0.04\pm0.02$ at visible to
mid-IR wavelengths where the flux is dominated by the smallest bound grains.
These values are comparable to the estimated thicknesses of many vertically
resolved debris discs, as is illustrated with the specific example of AU Mic.
For all systems with $h \sim h_{min}$, the presence (or absence) of embedded
perturbing bodies cannot be inferred from the vertical dispersion of the disc
