NEW OBSERVING FACILITIES E.G. ALMA AND SOON JWST HAVE BEEN PRODUCING AND WILL CONTINUE TO PRODUCE INCREASINGLY DETAILED INFORMATION ON DEBRIS DISK COMPOSITION AND STRUCTURE. IN ORDER TO PROPERLY INTERPRET AND FULLY EXPLOIT THESE AND OTHER DEBRIS DISK DATA THIS PROPOSAL WILL ADVANCE AND REFINE THE THEORY OF COLLISIONAL SIZE DISTRIBUTIONS BY SELF-CONSISTENTLY INCORPORATING PLANETESIMAL VELOCITIES INTO SIZE DISTRIBUTION CALCULATIONS. GIVEN SIZE DISTRIBUTION SCALE HEIGHT AND/OR VELOCITY DISPERSION MEASUREMENTS FOR A CERTAIN DISK THE PLAN IS TO THEN APPLY THE NEW THEORY TO CONSTRAIN THE DISK PLANETESIMALS BULK COMPOSITIONS AND THE MASS IN ANY NEARBY PLANETS INTERACTING GRAVITATIONALLY WITH THE DISK. THE SIZE AND VELOCITY DISTRIBUTIONS OF THE FOMALHAUT AND AU MIC DEBRIS DISKS WERE STUDIED VIA APPLICATIONS OF OUR THEORY TO ALMA AND HST OBSERVATIONS. THIS WORK ALONG WITH SIZE DISTRIBUTION MEASUREMENTS IN ~12 OTHER DISKS SUGGESTS THAT TWO DIFFERENT KINDS OF COLLISIONAL EVOLUTION MAY ALSO PLAY A ROLE IN VERY HOT (LARGE RANDOM PLANETESIMAL VELOCITIES) AND VERY COLD (SMALL RANDOM VELOCITIES) SYSTEMS: 1) CASCADES WHERE COLLISIONS LEAD TO SLOW BUT NON-ZERO VELOCITY DAMPING AND 2) CASCADES WHERE CHIPPING OFF OF SMALL FRAGMENTS FROM LARGER BODIES NOT COMPLETE COLLISIONAL DESTRUCTION FUELS THE CASCADE. WE PROPOSE TO REFINE OUR CASCADE THEORY TO INCLUDE THESE POSSIBILITIES APPLY THE REFINEMENTS IN A FULLER INTERPRETATION OF THE OBSERVATIONS AND DISSEMINATE OUR RESULTS IN THE SCIENTIFIC LITERATURE.