A commonly held perception is that an elite graduate degree can "scrub" a less prestigious but less costly undergraduate degree. Using data from the National Survey of College Graduates from 2003 through 2017, this paper examines the relationship between the status of undergraduate degrees and earnings among those with elite post-baccalaureate degrees. Few graduates of nonselective institutions earn post-baccalaureate degrees from elite institutions, and even when they do, undergraduate institutional prestige continues to be positively related to earnings overall as well as among those with specific post-baccalaureate degrees including business, law, medicine, and doctoral. Among those who earn a graduate degree from an elite institution, the present value of the earnings advantage to having both an undergraduate and a graduate degree from an elite institution generally greatly exceeds any likely cost advantage from attending a less prestigious undergraduate institution.