Five methods of factor rotation-Maxplane, Oblimax, Promax, Harris- Kaiser, and Varimax-were applied to four types of data-questionnaire, objeckive test, a physical problem, and a plasmode. In addition, the Maxplane procedure was followed in each case by Rotoplot-assisted visual robations. The results were compared with respect to simple structure (hyperplane percentages) and factor invaniance (congruence coefficient). It was concluded that, in general, the oblique methods were superior to Varimax in terms of simple structure although not consistently in terms of factor invariance. Among the oblique methods, the Rotoplot-assisted Maxplane usually resulted in the maximum simple structure at the f .10 hyperplane width but not consistently at either of the other two arbitrarily chosen widths. The unassisted Maxplane was generally excelled by the less expensive oblique methods both wiith respect to hyperplane count and factor invariance. The Harris-Kaiser method was generally more satisfadory in terms of the two criteria combined.