The coils described in this paper are assembled in two relatively thin flat stacks which are placed on each pole piece of a nuclear spin resonance magnet. One coil of each coil pair is in each of the two stacks, and each coil pair is so designed that the current circulating in it produces, in the airgap center, a correcting magnetic field describable by one of a set of spherical harmonics. The orthogonal properties of the spherical harmonics render possible substantially independent adjustments of the currents in the several coil pairs, when some spin resonance parameter such as line width is utilized to determine that individual optima are reached. Experimental coil stacks with 13 coil pairs, for the second, third, and zonal fourth harmonics, have been constructed, and preliminary results obtained by Rex Richards (Oxford) indicate that when a 4‐mm spin sample is used, this method can serve to reduce field inhomogeneities to less than 1 part in 108 with few sets of 13 current adjustments.