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This paper presents an effective full-wave procedure to optimize linearly polarized radial-line slot-array antennas. The procedure is based on a recursive method for solving large matrix equations known as the multiple sweep method of moments. As a result of this paper, new design suggestions have been introduced which greatly contribute to the performance improvement of this type of antennas. These elements are the arrangement of the slots in concentric ellipses instead of circles and a slight but crucial modification on the usual collocation of the reflection-canceling slots.