Connective mixing between the thin superficial hydrogen layer and the more massive and deeper helium layer is generally believed to be responsible for the increased number of non-DA white dwarfs relative to the number of DA below 10000K (see Sion 1984 and references therein). However, because of the spectroscopic invisibility of the helium lines at effective temperatures below 13000K, the true atmospheric composition of these cool stars remains somewhat uncertain. On theoretical grounds, studies of the evolution of white dwarfs on the cooling sequence have shown that if the hydrogen layer is thicker than ~10”6Me, convective mixing does not occur (Tassoul, Fontaine, and Winget 1988). Furthermore, the exact amount of helium pollution is very sensitive to the thickness of the hydrogen layer. It seems therefore imperative to evaluate to what extent DA stars below 13000K truly are hydrogen-rich. In line with our previous efforts geared toward an understanding of the atmospheric properties of the cool DA white dwarfs, we present new insights into the spectroscopic modelling of these cool stars, and also demonstrate, for a particular object, how the helium abundance might be determined.