We study experimentally the behaviour of a drop deposited on a conical fibre. It is shown that for wetting liquids, such a drop spontaneously moves towards the region of lower curvature. The driving force is measured and shown to be a gradient of Laplace pressure, which allows us to characterize the dynamics of these self-propelling drops. We conclude by discussing the efficiency of this device for drying a solid initially coated with a liquid film.