We derive a simple model, valid within the Boussinesq approximation, for the dynamics of small buoyant particles in stratified turbulence, in presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependency on the particle properties. On the contrary, small scale fractal clustering is found to depends on the particles relaxation time and is only slightly dependent on the flow stratification. The implications of our findings for the formation of thin phytoplankton layers are discussed.