Factorial experiments are done to measure the average effects of varying each of several factors (experimental conditions, independent variables) over fixed ranges of the other factors. Factors at two levels only are considered here. The system under study is assumed to permit the variation of only one factor per trial. Up to four factors may be of interest. The sequences proposed, of sizes 7–9, are easy to remember, simple to analyze, and straightforward to augment. Each result is compared with its immediate predecessor or successor only. Thus the three-factor one-at-a-time factorial follows the sequence. (1)1,a,ab,abc,bc,c, (1)2, where (1) means all factors at their low levels;ameans 1 factor,A, at its high level;abmeansAandBat high levels; and so forth.