Precise relative radial velocities (sigma approximately 20 m s-1) are presented for three K giants: alpha Tau, alpha Boo, and beta Gem. The data reveal periods of 233 days for alpha Boo, 643 days for alpha Tau, and 558 days for beta Gem. These periods are much too long to be due to radial pulsations. Currently, the only plausible explanations for these radial velocity variations are that they are due to rotational modulation by surface features (the expected rotation periods for these stars are of order the observed periods), nonradial pulsations, or planetary companions. Orbital solutions to the radial velocity variations yield companion masses in the range of 3 to 12 Jovian masses. However, the fact that all three stars exhibit similar periods and give comparable companion masses suggests that the variability is intrinsic to the star (either rotational modulation or pulsations). Phasing the radial velocity measurements of a Boo and a Tau by Walker et al. to our ephemeris results in a good agreement in both phase and amplitude with our radial velocity data. These long-term variations seem to have been present and coherent for at least the last 10 yr. The period of the relative radial velocity variations for a Boo is identical to the period of He I 10830 angstrom variations found by Lambert. This indicates that the observed radial velocity variations may be related to the chromospheric heating in these stars. Alpha Boo and alpha Tau show significant night-to-night changes in the radial velocity of up to 100 m s-1. This indicates the presence of short-term periods. However, the sampling pathology of our data is such that these periods cannot be well determined. Beta Gem shows no significant night-to-night variations.
