We reexamine the question of the short periods (approximately 109.3 s) observed in the ZZ Ceti star G226-29 by combining new period data obtained from our recent exhaustive adiabatic pulsation survey of DA white dwarfs with new spectroscopic determinations of the atmospheric parameters of that star. If, as suggested by the triplet structure of the 109.3 s peak in the Fourier spectrum of the light curve, the observed pulsations correspond to an l = 1 mode split by slow rotation, then we find that G226-29 must have a relatively thick hydrogen layer. Our best estimates suggest that the hydrogen layer mass in G226-29 is log q(H) congruent-to -4.4 +/- 0.2. The constraints on the hydrogen layer mass become less severe if the observed 109.3 s complex turns out to be an l = 2 or 3 mode (which could occur if some frequency components were excited with amplitudes below detectability levels). For an l = 2 mode, we find that log q(H) congruent-to - 6.6 + 0.2, while no useful constraint on the hydrogen layer mass can be obtained from the period data for an l = 3 mode. We suggest an observational test which should settle the issue of the l value of the 109.3 s mode in G226-29.