In dividing cells, kinetochores couple chromosomes to the tips of growing and shortening microtubule fibres and tension at the kinetochore-microtubule interface promotes fibre elongation. Tension-dependent microtubule fibre elongation is thought to be essential for coordinating chromosome alignment and separation, but the mechanism underlying this effect is unknown. Using optical tweezers, we applied tension to a model of the kinetochore-microtubule interface composed of the yeast Dam1 complex bound to individual dynamic microtubule tips. Higher tension decreased the likelihood that growing tips would begin to shorten, slowed shortening, and increased the likelihood that shortening tips would resume growth. These effects are similar to the effects of tension on kinetochore-attached microtubule fibres in many cell types, suggesting that we have reconstituted a direct mechanism for microtubule-length control in mitosis.