In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations. EB is substantially better than standard methods when rates have strong spatial and age patterns. We illustrate this method with estimates of age-specific fertility schedules for over 3,800 Brazilian municipalities.