New observational spectroscopic methods have made it possible to obtain radial velocities of eclipsing binary star components with unprecedented accuracy. Most of the improvement in accuracy is due to two techniques: (1) The use of optical fibers to scramble the spatial distribution of stellar brightness at the input end of the spectrometer, and to allow the spectrometer to be located off the telescope where its temperature and position can be stabilized. (2) The simultaneous exposure of the comparison emission-tube light through a separate fiber or pair of fibers adjacent to the stellar fiber continuously during the stellar exposure. Any changes in the response of the spectrometer during the exposure then affect the stellar and adjacent comparison spectra in almost exactly the same way.