We have determined spectroscopic orbital elements for 13 systems - 10 single-lined binaries and three double-lined binaries. For the three binaries with previously published spectroscopic orbits, we have computed improved or comparable elements. While two systems have relatively short periods between 10 and 19 days, the remaining systems have much longer periods ranging from 604 to 9669 days. One of the single-lined systems, HD 142640, shows both short-period and long-period velocity variations and so is triple. For three systems - HD 59380, HD 160933, and HD 161163 - we have combined our spectroscopic results with Hipparcos astrometric observations to obtain astrometric orbits. For HD 14802 we have determined a joint orbital solution from spectroscopic velocities and interferometric observations. The orbits given here will be useful in combination with future interferometric and Gaia satellite observations.