We present an analysis of three years of precision radial velocity (RV) measurements of 160 metal-poor stars observed with HIRES on the Keck 1 telescope. We report on variability and long-term velocity trends for each star in our sample. We identify several long-term, low-amplitude RV variables worthy of followup with direct imaging techniques. We place lower limits on the detectable companion mass as a function of orbital period. Our survey would have detected, with a 99.5% confidence level, over 95% of all companions on low-eccentricity orbits with velocity semiamplitude K>~100m/s, or M_p_sini>~3.0M_J_(P/yr)^(1/3)^, for orbital periods P<~3yr. None of the stars in our sample exhibits RV variations compatible with the presence of Jovian planets with periods shorter than the survey duration.