The usual reason for using the Q-sort technique has been to acquire information about the subjects doing the sorting, but this paper concerns the construction of a Q-sort which deals with information about the items comprising the Q-sort; more specifically, the knowledge and ability competencies of teachers of graduate level courses. A list of competency items was compiled from the state requirements for certification, the course descriptions in the university catalog, the faculty involved, and a critical incident questionnaire completed by a sample of students. The items were placed on the backs of cards; students were asked to sort them as to relative importance; and teachers were asked to sort them using their own level of adequacy as the criterion. In this way, the level of adequacy for each competency for each teacher can be determined and compared with the results of the student data, identifying gaps between what the students feel is important for the faculty to be competent in and what the faculty feel they are actually competent in. (BW)