The production of W bosons at large transverse momentum in p¯p collisions is studied. The next-to-leading order cross section in this region is dominated by threshold soft-gluon corrections. The transverse momentum distribution of the W at the Tevatron is modestly enhanced when next-to-next-to-leading-order soft-gluon corrections are added, and the dependence on the factorization and renormalization scales is significantly reduced.