Precise absolute radial velocities have been measured for several hundred late-type stars at Mt John University Observatory with the 1-m telescope, fiber-fed échelle spectrograph, and Thomson CCD. Six échelle orders in the green (5000−5600 Å) are used. Many delicate steps have been undertaken in order to maintain exactly the same conditions, both in recording and reducing the spectra, over a period of 18 months. A cross-correlation technique with theoretical spectra computed by R. L. Kurucz has been chosen to determine the absolute radial velocities. Blue sky spectra have been used to monitor systematic zero-point fluctuations from one observing run to another. An additional correlation between the measured velocities and average number of A/D units in the continuum has been discovered and used for fine adjustments, significantly improving the results. A random uncertainty of 10–20 ms−1 has been achieved for stellar spectra having intrinsically constant radial velocities.