The intrinsic anomalous Hall conductivity in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent ab initio studies found that it was necessary to sample the Brillouin zone at millions of k -points to converge the calculation. We present an efficient first-principles approach for computing this quantity. We start out by performing a conventional electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse k -poi...