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 (Teff=11,800+/-200 K and logg=7.87+/-0.05) and for HE 1258+0123 (Teff=11,410+/-200 K and logg=8.04+/-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 logg-Teff 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. Based, in part, on observations gathered at the European Southern Observatory, La Silla, Chile.