Fries and Hunter (1980) presented a practical algorithm for selecting standard 2n–mfractional factorial designs based on a criterion they called “minimum aberration.” In this article some simple results are presented that enable the Fries–Hunter algorithm to be used for a wider range ofnandmand for designs with factors atplevels wherep≥ 2 is prime. Examples of minimum aberration 2n–mdesigns with resolutionR≥ 4 are given form,n–m< 9. A matrix is given for generating 3n–mdesigns withm,n–m≤ 6, which have, or nearly have, minimum aberration.