We present analysis of precision radial velocities (RV) of 1134 mostly red giant stars in the southern sky, selected as candidate astrometric grid objects for the Space Interferometry Mission (SIM). Only a few (typically, 2 or 3) spectroscopic observations per star have been collected, with the main goal of screening binary systems. The estimated rate of spectroscopic binarity in this sample of red giants is 32% at the 0.95 confidence level, and 46% at the 0.75 confidence. The true binarity rate is likely to be higher, because our method is not quite sensitive to very wide binaries and low-mass companions. The estimated lower and upper bounds of stellar RV jitter for the entire sample are 24 and 51 m/s, respectively; the adopted mean value is 37 m/s. A few objects of interest are identified with large variations of radial velocities, implying abnormally high mass ratios.