We present SiFTO, a new empirical method for modeling Type Ia supernova (SN Ia) light curves by manipulating a spectral template. We make use of high-redshift SN data when training the model, allowing us to extend it bluer than rest-frame U. This increases the utility of our high-redshift SN observations by allowing us to use more of the available data. We find that when the shape of the light curve is described using a stretch prescription, applying the same stretch at all wavelengths is not an adequate description. SiFTO therefore uses a generalization of stretch which applies different stretch factors as a function of both the wavelength of the observed filter and the stretch in the rest-frame B band. We compare SiFTO to other published light-curve models by applying them to the same set of SN photometry, and demonstrate that SiFTO and SALT2 perform better than the alternatives when judged by the scatter around the best-fit luminosity distance relationship. We further demonstrate that when SiFTO and SALT2 are trained on the same data set the cosmological results agree.