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Abstract Does the Halbach magnetization rotation rule that is used for designing circular magnet arrays for achieving the best homogeneity hold also for an elliptical or other non-circular cross-section? In this article, it is shown that a new numerically optimized magnetization rotation rule can provide more than three orders of magnitude improvement in field homogeneity as compared to a Halbach configuration for elliptical systems. Further it is demonstrated that such optimized magnetization rules can be easily derived in an intuitive way by studying virtual permanent magnets of a similar cross-section as the desired magnet array. This is coined as a permanent magnet hypothesis. Finally, it is shown that the applicability of this technique is not limited to circular or elliptical systems but can be applied to any arbitrarily shaped cross-section.