The 2001 U.S. Supreme Court Case of Falvo v. Owasso School System (Owasso Independent School District No I-011 v. Falvo) has focused national attention on the common classroom practice of peer-grading. In a unanimous decision the court reaffirmed the popular view that students grading each others' tests is valuable, saving teachers' time and augmenting student learning. Our study puts these presumed benefits to the test in 4 middle school science classrooms. We compared teacher-assigned grades to those awarded either by students to themselves or by their peers. By training students to grade with the help of a scoring rubric, a very high correlation was obtained between students and their teacher on test questions (r = 0.91 to 0.94). We found patterns of bias when students assigned grades. When grading others, students awarded lower grades to the best performing students than their teacher did. When grading themselves, lower performing students tended to inflate their own low scores. Performance on an unannounced, 2nd administration of the same test 1 week later measured the degree to which student-grading resulted in any increased understanding. Students who graded their peers' tests did not gain significantly more than a control group of students who did not correct any papers but simply took the same test again. Those students who corrected their own tests improved dramatically. Self-grading and peer-grading appear to be reasonable aids to saving teachers' time. Self-grading appears to result in increased student learning; peer-grading does not.