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, two or three) 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 per cent at the 0.95 confidence level, and 46 per cent 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 51m/s, respectively; the adopted mean value is 37m/s. A few objects of interest are identified with large variations of RV, implying abnormally high mass ratios.