The process of phase correction for emission line spectra with high signal-to-noise ratios has remained a surprisingly complicated problem that can seriously affect the precision of data derived from Fourier transform emission spectra. Traditional methods, using a low resolution phase spectrum can produce spectra that show systematic errors in line positions and profiles. An improved phase correction strategy has been developed for and tested with infrared, visible, and ultraviolet emission line sources. A carefully apodized transform of relatively high resolution provides the phase data. A discriminator is used to restrict the data to those points that have a sufficiently high signal-to-noise ratio to provide a reliable phase estimate, and a smooth phase function is obtained by fitting a polynomial to these points. Some characteristics of real interferograms that complicate this simple picture are discussed.