This is a trial to test whether treadmill training can be used to improve the "walking" of patients with partial spinal cord injury. While on the treadmill, patients will be partially supported through the use of a specially designed harness attached to an overhead lift (also called Body Weight Supported Treadmill Training, BWSTT). Patients who enroll in this study will be randomly assigned to either the experimental group, which receives 12 weeks of this specialized treadmill training with regular physical therapy, or to the control group, which receives 12 weeks regular physical therapy. The ability of the patients to "walk" will be measured before and after treatment as well as 6 and 12 months later, using standard tests that examine mobility independence and speed of ambulation. The trial takes place across five sites in the US and Canada. Patients eligible for this trial will have had a traumatic spinal cord injury within 8 weeks of trial entry.