We are interested in the behaviour of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold, with Kahler classes approaching the boundary of the Kahler cone. The case when the volume approaches zero is especially interesting since the corresponding complex Monge-Ampere equation degenerates in the limit. If the Calabi-Yau manifold is the total space of a holomorphic fibration, the Ricci-flat metrics collapse to a metric the base, which `remembers' the fibration structure.