The ZZ Ceti star L 19-2 is a stable pulsator whose light curve has now been deciphered with the help of over 300 hours of white light, high-speed photometry (O’Donoghue and Vamer 1982, 1987, hereafter ODV). The analysis indeed reveals the presence in the light curve of five coherent oscillations, with periods ranging from 113s to 350s. Among those, the 192s oscillation possesses three components, almost equally separated in frequency. Most importantly, the slight, but statistically significant, inequality in the frequency spacing of the triplet has been interpreted by these authors as second-order splitting of rotationally-perturbed g-mode oscillations. And indeed, the measured splitting appears consistent with the theoretical predictions of Chlebowski (1978), which are based on somewhat archaic white dwarf models. As pointed out by ODV, it is clearly of great interest to investigate 1) to what extent theoretical predictions based on more realistic, current-generation white dwarf models agree with ODVs identification, and 2) to what extent such second order effects can, eventually, be used to identify individual pulsation modes or constrain the structural parameters of variable white dwarf stars. Motivated by these questions, we have initiated a study of second-order effects due to rotation in ZZ Ceti stars, and we report here the first results of this program.