In a letter published in ApJL, we improve the current understanding of the atmospheres of brown dwarfs, especially cold ones with spectral types T and Y, whose modeling is a current challenge. Silicate and iron clouds are believed to disappear at the photosphere at the L/T transition, but cloudless models fail to reproduce correctly the spectra of T dwarfs, advocating for the addition of more physics, e.g., other types of clouds or internal energy transport mechanisms. We use a one-dimensional radiative/convective equilibrium code ATMO to investigate this issue. This code includes both equilibrium and out-of-equilibrium chemistry and solves consistently the PT structure. Included opacity sources are H2-H2, H2-He, H2O, CO, CO2, CH4, NH3, K, Na, and TiO, VO if they are present in the atmosphere. We show that the spectra of Y dwarfs can be accurately reproduced with a cloudless model if vertical mixing and NH3 quenching are taken into account. T dwarf spectra still have some reddening in, e.g., J–H, compared to cloudless models. This reddening can be reproduced by slightly reducing the temperature gradient in the atmosphere. We propose that this reduction of the stabilizing temperature gradient in these layers, leading to cooler structures, is due to the onset of fingering convection, triggered by the destabilizing impact of condensation of very thin dust.