Appropriate data distribution has been found to be critical for obtaining good performance on Distributed Memory Multicomputers like the CM-5, Intel Paragon and IBM SP-1. It has also been found that some programs need to change their distributions during execution for better performance (redistribution). This work focuses on automatically generating efficient routines for redistribution. We present a new mathematical representation for regular distributions called PITFALLS and then discuss algorithms for redistribution based on this representation. A significant contribution of this work is the ability to handle arbitrary source and target processor sets while performing redistribution; another is the ability to handle arbitrary dimensionality for the array being redistributed in a sealable manner. The results presented show low overheads for our redistribution algorithm as compared to naive runtime methods.< >