A novel radio-frequency (RF) pulse design algorithm is presented that generates fast slice-selective excitation pulses that mitigate B+1 inhomogeneity present in the human brain at high field. The method is provided an estimate of the B+1 field in an axial slice of the brain and then optimizes the placement of sinc-like "spokes" in kz via an L1-norm penalty on candidate (kx, ky) locations; an RF pulse and gradients are then designed based on these weighted points. Mitigation pulses are designed and demonstrated at 7T in a head-shaped water phantom and the brain; in each case, the pulses mitigate a significantly nonuniform transmit profile and produce nearly uniform flip angles across the field of excitation (FOX). The main contribution of this work, the sparsity-enforced spoke placement and pulse design algorithm, is derived for conventional single-channel excitation systems and applied in the brain at 7T, but readily extends to lower field systems, nonbrain applications, and multichannel parallel excitation arrays. Copyright (c) 2008 Wiley-Liss, Inc.