We have measured the central stellar velocity dispersions of 33 nearby spiral and elliptical galaxies, using a straightforward template-fitting algorithm operating in the pixel domain. The spectra, obtained with the Double Spectrograph at Palomar Observatory, cover both the Ca triplet and the Mg b region, and we present a comparison of the velocity dispersion measurements from these two spectral regions. Model fits to the Ca triplet region generally yield good results with little sensitivity to the choice of template star. In contrast, the Mg b region is more sensitive to template mismatch and to details of the fitting procedure such as the order of a polynomial used to match the continuum shape of the template to the object. As a consequence of the correlation of the [Mg/Fe] ratio with velocity dispersion, it is difficult to obtain a satisfactory model fit to the Mg b lines and the surrounding Fe blends simultaneously, particularly for giant elliptical galaxies with large velocity dispersions. We demonstrate that if the metallicities of the galaxy and template star are not well matched, then direct template-fitting results are improved if the Mg b lines themselves are excluded from the fit and the velocity dispersion is determined from the surrounding weaker lines.