One study of 1990s data found that, all else equal, poorer students received no lift relative to affluent ones. Mr. Espenshade found that low-income minorities were somewhat more likely to gain admission than similar higher-income minorities but that lower-income whites received no advantage. In effect, poor and middle-income students are rejected, while others with the same scores and grades — legacies, athletes and minorities, often from privileged backgrounds — are admitted.

As a result, elite public and private colleges remain dominated by affluent students. Some colleges probably have more students from the top 2 percent of the income distribution than the bottom 50 percent.

The current system has left colleges in legal jeopardy because of both the conservative bent of today’s judiciary and the high legal burden that the law places on any race-based program. In a 1978 case, the justices called for “strict scrutiny” of such programs. In his 2003 dissent, Justice Kennedy argued that colleges did not meet this standard. Instead, he wrote, race often determined admissions decisions.

As he said to the University of Texas’s lawyer during arguments in October, “What you’re saying is that what counts is race above all.”

The Kennedy dissent leaves the door open to affirmative action, but only a form that makes the explicit consideration of race a last resort. Other factors would have to come first. As it happens, there are several officially race-neutral factors that would raise no constitutional risk — and help many minority applicants.

The most obvious is income. But others may be more important. If colleges gave students credit for coming from a low-income ZIP code, black and Latino students would benefit enormously, as they would from the consideration of wealth and family status. Only 27 percent of white students grow up in a single-parent family, compared with 60 percent of black children and 34 percent of Latino children.

One possible outcome is that the court will force colleges to show they have tried these forms of affirmative action before they turn to race. Another is a decision holding that racial preferences can be no larger — in terms of SAT points, for instance — than class preferences, says Stuart Taylor Jr., a co-author of a book critical of affirmative action.