Reconstructions of the relative positions of the India and Eurasia plates, using recently revised histories of movement between India and Somalia and between North America and Eurasia and of the opening of the East African Rift, show that India's convergence rate with Eurasia slowed by more than 40% between 20 and 10 Ma. Much evidence suggests that beginning in that interval, the Tibetan Plateau grew outward rapidly and that radially oriented compressive strain in the area surrounding Tibet increased. An abrupt increase in the mean elevation of the plateau provides a simple explanation for all of these changes. Elementary calculations show that removal of mantle lithosphere from beneath Tibet, or from just part of it, would lead to both a modest increase in the mean elevation of the plateau of ∼1 km and a substantial change in the balance of forces per unit length applied to the India and Eurasia plates.