Evidence is presented from a factor analytic study of a large sample using scores based on the AVL Study of Values and the Myers-Briggs Type Indicator, displaying a four-dimensional, interlocking structure for the two instruments. The MBTI scores define a simple structure with respect to which the AVL scores exhibit a bi-polar structure. The AVL scores may be regarded as depending on the third-order interaction of the four basic dimensions. Both the interlocking form of structure and a significant proportion of its details were anticipated in advance of the present analysis. If the model is valid, it implies the existence of sixteen distinct value systems, a majority of which appear to have been merged or overlooked in the construction of the AVL. Certain of these value systems have special properties causing them to be quite elusive. The AVL and the MBTI were chosen for study because both are based on typological thinking about personality. The results of the investigation indicate that such thinking can lead to consistent concepts that are worthy of further study.