Low-concentration polymers can strongly influence crystal growth in small-molecule glasses, a phenomenon important for improving physical stability against crystallization. We measured the velocity of crystal growth in two molecular glasses, nifedipine (NIF) and o-terphenyl (OTP), each doped with four or five different polymers. For each polymer, the concentration was fixed at 1 wt % and a wide range of molecular weights was tested. We find that a polymer additive can strongly alter the rate of crystal growth, from a 10-fold reduction to a 10-fold increase. For a given polymer, increasing molecular weight slows down crystal growth and the effect saturates around DP = 100, where DP is the degree of polymerization. For all the systems studied, the polymer effect on crystal growth rate forms a master curve in the variable (T - T)/T, where T is the glass transition temperature and T is the crystallization temperature. These results support the view that a polymer's effect on crystal growth is controlled by its segmental mobility relative to the host-molecule dynamics. In the proposed model, crystal growth rejects impurities and creates local polymer-rich regions, which must be traversed by host molecules to sustain crystal growth at rates determined by polymer segmental mobility. Our results do not support the view that host-polymer hydrogen bonding plays a controlling role in crystal growth inhibition.