We report on the settling of loosely packed, cohesionless granular material under mechanical vibrations. Monodisperse spherical beads were confined to a long vertical cylinder that was driven by an electromagnetic vibration exciter. Under vibrations the bead packing evolves from an initial, low-density configuration towards higher density. Ramping the vibration intensity repeatedly up and back down again reveals the existence of both an irreversible and a reversible branch in the response. The reversible branch represents a steady state in which the packing density depends monotonically on the vibration intensity. We have investigated the bead size, depth, and ramp rate dependence of the compaction process. Our results indicate how the occupied volume fraction can be optimized by slowly reducing the vibration intensity along the reversible branch.