An optoelectronic shuffle-exchange interconnection system consists of many duplicate stages of shuffle optics and electronic bypass-exchange switches. Haney1 has suggested that for "reasonable" size arrays, an optical shuffle has a great deal of unutilized space-bandwidth product (SBWP). Thus, instead of replicating the optics, we could use a single lens array to perform the shuffle for all stages of the system. We have developed a simple procedure to optimize the packing capability of a free-space perfect shuffle2 to define reasonable array sizes, and where unutilized SBWP actually exists.