Interest in uniformly illuminated (isophoric) density-tapered planar antenna arrays has recently revived. For arrays consisting of concentric rings of elements, we present a nonstochastic algorithm that calculates ring radii for generation of pencil beams without the need for prior specification of the number of rings. Use of the algorithm is illustrated by application to multibeam coverage of the Earth. The use of its results as the starting point of a stochastic optimization has led to complete solution of a hitherto recalcitrant synthesis problem.