The creation of racially diverse colleges at all levels of selectivity has proven to be no small task, even with the legal use of race-conscious affirmative action. As evidenced in the postsecondary destinations of the high school class of 2004, very selective schools (those with Barron's Selectivity rankings of 1, 2 or 3) have many more White, and many fewer Black and Hispanic, students than the population of 18-year-olds overall. However, the trend of decreasing diversity with increasing selectivity is not strictly monotonic: the most selective schools (Barron's 1s) are slightly more diverse than the schools just below them in the selectivity rankings. In these Barron's 1 schools there is suggestive evidence of successful (race-based) affirmative action policies. Given the apparently modest results of explicitly race-based affirmative action, the construction of race-neutral policies that replicate, or even improve upon, these levels of diversity presents a daunting challenge. The goal of this study is to inform the current affirmative action debate with evidence from sophisticated simulation models in which the authors vary how colleges weigh race and class in the admission decision process. This model is able to take into account many of the complexities and interrelated dynamics of the college admissions process, such as uncertainty over college or student quality, learning over time, and strategic application submission. Results from the simulations suggest at least three important patterns: (1) unless SES-based affirmative action policies use a very large bump, these policies are unlikely to result in the same racial composition in colleges as under current race-based affirmative action policies; (2) socioeconomic affirmative action results in a moderate-to-substantial reduction in the average resources of students enrolled at elite colleges, and are thus effective at increasing socioeconomic diversity; and (3) information plays a large, and perhaps previously unrecognized, role in the sorting of minority students into colleges; the application behavior of students responded much more effectively to affirmative action policies when those policies were made explicit to students. Three figures are appended.