  We review at length the longstanding problem in the spectroscopic analysis of
cool hydrogen-line (DA) white dwarfs (Teff < 13,000 K) where gravities are
significantly higher than those found in hotter DA stars. The first solution
that has been proposed for this problem is a mild and systematic helium
contamination from convective mixing that would mimic the high gravities. We
constrain this scenario by determining the helium abundances in six cool DA
white dwarfs using high-resolution spectra from the Keck I 10-m telescope. We
obtain no detections, with upper limits as low as He/H = 0.04 in some cases.
This allows us to put this scenario to rest for good. We also extend our model
grid to lower temperatures using improved Stark profiles with non-ideal gas
effects from Tremblay & Bergeron and find that the gravity distribution of cool
objects remains suspiciously high. Finally, we find that photometric masses
are, on average, in agreement with expected values, and that the high-log g
problem is so far unique to the spectroscopic approach.
