We review at length the longstanding problem in the spectroscopic analysis of cool hydrogen-line ( DA ) white dwarfs ( T _ { eff } < 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 .