The largest gains in graduation rates over the past decade have been accomplished at open-access or nearly open-access colleges and universities. In addition, states could see even bigger increases if they directed their policies and supports toward improving graduation rates at these nonselective institutions. These findings from the author's research at Vanderbilt University challenge a commonly held notion that the best way to increase graduation rates is to make colleges more selective, since highly selective colleges tend to have higher rates of completion. This research finds that nonselective colleges and universities (those that accept at least 80% of applicants) are leading the way in improving graduation rates. These colleges and universities account for most of the increases in completion rates in 33 states. In 16 states, these institutions account for more than 75% of the increases. This discovery has broad implications for state policy, particularly under these stringent budgetary conditions. Open-access or nearly open-access colleges are typically where the greatest improvements in completion rates can be made at the lowest cost, partly because the cost per student is lower than at more selective research universities. However, nonselective colleges and universities are also most vulnerable to economic downturns, since they are funded primarily by state appropriations and tuition. (Contains 3 figures.)