We examine the possibility that stars in the nuclei of galaxies could be 'ground down' into short-period orbits, by interaction with a disc around a central massive black hole. A star on a highly eccentric orbit, which passed close to the hole, would lose energy and momentum in passing through the disc. The cumulative effect of many passages would bring the star into a circular orbit corotating with the disc. The star would then either open up a gap in the disc (if the disc is thinner than the star's Roche radius and the viscosity in the disc is sufficiently low), or accrete material from the disc. By these processes, stars could, without prior disruption, acquire orbits whose binding energy to the hole greatly exceeds their self-binding energy, and may even be relativistic. There are possible implications for the fuelling and variability of AGN. In particular, a star on a tight bound orbit could modulate the luminosity in a periodic fashion.