We consider the transverse-momentum (q) distribution of Drell-Yan lepton pairs produced in hadron collisions. At small values of q, we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. At intermediate and large values of q, we consistently combine resummation with the known next-to-leading order perturbative result. All perturbative terms up to order αS2 are included in our computation which, after integration over q, reproduces the known next-to-next-to-leading order result for the Drell-Yan total cross section. We show and discuss the reduction in the scale dependence of the results with respect to lower-order calculations, estimating the corresponding perturbative uncertainty. We present a preliminary comparison with Tevatron Run II data.