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-g,T-polymer - T-g,T-host)/T-cryst, where T-g is the glass transition temperature and T-cryst 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.