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Although top-down selection is the gold standard for making personnel decisions, several administrative assumptions must be met for it to be effective. We discuss three of these assumptions and test two of them: (1) top applicants will accept an offer, and (2) the time organisations give applicants to consider an offer will not influence the availability of next-tier applicants. We also examine the effectiveness of top-down selection by comparing it to an administratively simpler procedure, random selection above a threshold. Using archival admissions data from three university graduate psychology programs, we found that top applicants were less likely to accept an offer; however, waiting time did not influence applicant availability. In comparing the quality of applicants actually selected (with a top-down procedure) with the quality of applicants selected at random (from above five progressively stringent thresholds), we found that at higher admission thresholds, random selection resulted in better or equal quality applicants as top-down selection, depending on the criteria. We discuss implications for future research and practice.