New astrometric-spectroscopic orbital solutions for the single-line K-giant binaries beta Reticuli (P~5.2yr, e=0.3346+/-0.0004) and nu Octantis (P~2.9yr, e=0.2358+/-0.0003) have been derived based on high-precision spectroscopic radial velocities (RVs) and the Hipparcos astrometry.