We present a strategy to identify several thousand stars that are astrometr
ically stable at the microarcsecond level for use in the Space Interferomet
ry Mission (SIM) astrometric grid. The requirements on the grid stars make
this a rather challenging task. Taking a variety of considerations into acc
ount, we argue for K giants as the best type of stars for the grid, mainly
because they can be located at much larger distances than any other type of
star owing to their intrinsic brightness. We show that it is possible to i
dentify suitable candidate grid K giants from existing astrometric catalogs
. However, double stars have to be eliminated from these candidate grid sam
ples, since they generally produce much larger astrometric jitter than tole
rable for the grid. The most efficient way to achieve this is probably by m
eans of a radial velocity survey. To demonstrate the feasibility of this ap
proach, we repeatedly measured the radial velocities for a preselected samp
le of 86 nearby Hipparcos K giants with precisions of 5-8 m s(-1). The dist
ribution of the intrinsic radial velocity variations for the bona fide sing
le K giants shows a maximum around 20 m s(-1), which is small enough not to
severely affect the identification of stellar companions around other K gi
ants. We use the results of our observations as input parameters for Monte
Carlo simulations on the possible design of a radial velocity survey of all
grid stars. Our favored scenario would result in a grid which consists to
68% of true single stars and to 32% of double or multiple stars with period
s mostly larger than 200 years, but only 3.6% of all grid stars would displ
ay astrometric jitter larger than 1 mu as. This contamination level is prob
ably tolerable.