Allowing students to grade their own homework promises several advantages to both students and instructors. But does such a policy make sense? This paper reports the results of an experiment in which eight separate assignments completed by approximately 80 students were first graded by the students using a grading rubric, and then re-graded by a teaching assistant, using this same rubric. The study found that the differences observed in the two sets of data were statistically significant, but (in the author's opinion) acceptably small. The study also confirmed observations by earlier researchers that students who generously grade their work tend to fall among the lower-performing individuals in a class.