Responses of 392 students to the Eysenck Personality Inventory were analyzed using conventional factor-analytic techniques and a nonmetric multidimensional scaling method. Rotating the first two factors gave a result clearly comparable with an earlier third-order analysis, while a three-factor rotation neatly clustered the original Extraversion, Neuroticism, and Lie scale items. A three-dimensional non-metric analysis appeared to provide no more information for users of the questionnaire than was given by a comparable two-dimensional analysis which had produced a solution closely resembling that of the two-factor rotation. The conclusion reached was that psychometrically useful information may be more readily revealed by simple and rationally restricted analyses than by exhaustive, more complex, and higher order solutions.