Remediation is one of the largest single interventions intended to improve outcomes for underprepared college students, yet little is known about the remedial screening process. Using administrative data and a rich predictive model, we find that severe mis-assignments are common using current test-score-cutoff-based policies, with "underplacement" in remediation much more common than "overplacement" college courses. Incorporating high school transcripts into the process could significantly reduce placement errors, but adding test scores to already available high school data often provides little marginal benefit. Moreover, the choice of screening policy has significant implications for the racial and gender composition of college-level courses. Finally, the use of more accurate screening tools would enable institutions to remediate substantially fewer students without compromising college success.