  Instruments achieve sharper and finer observations of micron-in-size dust
grains in the top layers of young stellar discs. To provide accurate models, we
revisit the theory of dust settling for small grains, when gas stratification,
dust inertia and finite correlation times for the turbulence should be handled
simultaneously. We start from a balance of forces and derive distributions at
steady-state. Asymptotic expansions require caution since limits do not
commute. In particular, non-physical bumpy distributions appear when turbulence
is purely diffusive. This excludes very short correlation times for real discs,
as predicted by numerical simulations.
