Many egalitarians believe that there is a pro tanto reason to remedy inequalities of opportunity in access to higher education. This consensus, I argue, masks practical disagreement among egalitarians: in many real-world choice contexts, egalitarians will disagree about which policies are to be endorsed, both from the point of view of equality and all things considered. I focus my discussion on a real-world case (the "big squeeze"--so-called because the children of well-off families "squeeze out" the children of less well-off families from access to highly selective US universities) that has recently been discussed by Amy Gutmann. I argue that while (a) the "big squeeze" is condemned by the ideal of equal opportunity, nevertheless (b) different egalitarians will favor different policies in response to the "big squeeze," and (c) one intuitive, and apparently egalitarian, response lacks support from most plausible egalitarian views.