In the technique developed by K. G. Joreskog to solve the problem for oblique rotation to a specified simple structure, the basic concept is that the simple structure solution itself is determined only by the zero coefficients of the reference-structure matrix and not by the coefficients of non-zero magnitude. Following this, prior information about the desired simple structure is taken into account to impose zeros on some of the factor loadings. This way an n x r target matrix H is built with the zero elements specified and the others unspecified. This specific Procrustean rotation involves r eigenproblems. When prior information for the desired solution is not available, additional efforts are required to construct a target. A new strategy is proposed for this purpose, applying the technique of vector majorization. The constructed target matrix H has the same form as in Joreskog's work, but with all elements specified (both zeros and non-zeros), which transforms Joreskog's specific Procrustean rotation into a normal Procrustean rotation that enables the application of any well-known procedure for Procrustean rotation, and thus, avoiding the eigenproblems. A slightly different problem can also be solved when only the number of zeros in the target is known. All computational examples are based on 24 psychological tests of Holzinger and Harman. There are seven tables of example data. (SLD)