We report the discovery of two new ZZ Ceti pulsators , LP 133 - 144 and HE 1258 + 0123 , selected on the basis of model atmosphere fits to optical spectroscopic data . The atmospheric parameters for LP 133 - 144 , T _ { eff } = 11 , 800 \pm 200 K and \log g = 7.87 \pm 0.05 , and for HE 1258 + 0123 , T _ { eff } = 11 , 410 \pm 200 K and \log g = 8.04 \pm 0.05 , place them within the empirical boundaries of the ZZ Ceti instability strip . This brings the number of known ZZ Ceti stars to a total of 36 , a quarter of which have now been discovered using the spectroscopic approach for estimating their atmospheric parameters . This method has had a 100 % success rate so far in predicting the variability of candidate ZZ Ceti stars . We have also analyzed additional spectra of known nonvariable white dwarfs in the vicinity of the ZZ Ceti instability strip . Our study further strengthens the idea that ZZ Ceti stars occupy a pure region in the \log g - T _ { eff } plane , a region where no nonvariable stars are found . This result supports the thesis that ZZ Ceti pulsators represent a phase through which all DA stars must evolve .