Methods and devices are disclosed for processing stromal precursor cells (i.e., cells which can differentiate into connective tissue cells, such as in muscles, ligaments, or tendons) which can be obtained from fatty tissue extracts obtained via liposuction. Normal processing of a liposuction extract involves centrifugation, to concentrate the stromal cells into a semi-concentrated form called “spun fat”. That “spun fat” can then be treated by mechanical processing (such as pressure-driven extrusion through 0.5 mm holes) under conditions which can gently pry the stromal cells away from extra-cellular collagen fibers and other debris in the “spun fat”. The extruded mixture is then centrifuged again, to separate a highly-enriched population of stromal cells which is suited for injection back into the patient (along with platelet cells, if desired, to further promote tissue repair or regeneration).