We present a new generation of model atmospheres and synthetic spectra appropriate to the study of cool DA white dwarfs. The thermodynamic structure of the model atmospheres is calculated in LTE, with a standard complete linearization technique modified to take into account the energy transport by convection. The computed grid covers a range of 5000 less-than-or-equal-to T(eff) 12,000 K, 7.5 less-than-or-equal-to log less-than-or-equal-to 8.5 and O less-than-or-equal-to N(He)/N(H) less-than-or-equal-to 25. The emergent fluxes are calculated with the new occupation probability formalism of Hummer and Mihalas; this provides an improved theoretical framework for the computation of detailed atomic level populations which permits a careful analysis of the gravity- and helium-sensitive high Balmer lines. A comparison with results based on older, less satisfactory, formalisms reveals that this improved treatment leads to significant differences not only in the predicted line profiles, but also in the absolute continuum flux. These new synthetic spectra are used to study some of the systematic properties of the atmospheres of cool DA white dwarfs.