Over the years, a number of rationales have been advanced to solve the problem of "blind" oblique factor transformation. By blind transformation is meant the transformation of orthogonal--and often interpretively ineffectual--factors to a position usually dictated by Thurstone's principles of simple structure, but not influenced by a priori structural hypotheses. The major purpose of this paper is to examine the class of oblique solutions Harris and Kaiser found to have greatest potential--their "Case II" set--and to ascertain whether this formulation can provide solutions better than those currently obtained by the widely-used representatives of this class. In the process, a new algorithm which results in a single Case II solution is identified, and the efficacy of this representative of the class is examined. Certain features of the component matrices are explicated, and an iterative procedure is presented for their simultaneous solution. Illustrative examples are presented, based on both this iterative procedure and other Case II formulations. Implications for practice and further research are discussed. (Author/CTM)