This is a randomized Phase II trial investigating the optimal timing of delivery of neoadjuvant therapy, in order to maximize the proportion of patients with distal rectal cancer who may be cured while preserving the rectum. Patients with distal rectal cancer who are candidates for a coloanal anastomosis or abdominoperineal excision will be randomized to receive neoadjuvant chemotherapy before (induction arm) or after (consolidation arm) chemoradiation. Patients will be restaged 4 to 6 weeks after completing all neoadjuvant therapy. Those with incomplete tumor response will undergo a total mesorectal excision. Patients with complete tumor response will be observed, and will have a total mesorectal excision only if they develop signs of tumor relapse during follow-up.