And at Lowell High School in San Francisco, parents of the growing population of Chinese-American students complain that their children must score higher on the examination for admission than whites and other Asians to prevent exceeding their share of a court-ordered racial quota.
"It's not a racial issue. It's a fairness issue," said Michael McLaughlin, a lawyer who filed a federal lawsuit when his daughter, Julia, was turned down by Boston Latin despite her qualifying score. "I'd feel the same if blacks were not let in because there was a quota for whites."
Roland Quan, a Chinese-American graduate of Lowell High School whose son is now in the 10th grade there, said he would be willing to accept a preference for black and Hispanic students, "but we think that everyone else should have to compete equally".
Quotas based on race or gender have been under fire in the United States, and the disputes in Boston and San Francisco are at the centre of increasing opposition to mandated desegregation of the schools.
Boston Latin is the nation's oldest public high school and one of the best with 98 per cent of its graduates going on to college.
The comparable Lowell is the oldest public high school west of the Mississippi River and the principal feeder school for the highly rated University of California at Berkeley.
"Such controversies are at the cutting edge, to use an over-used phrase, of the law as it applies to education," said Judge W Arthur Garrity, who will hear the Boston Latin case.
The two disputes date back to the 1970s and 1980s, when federal judges ordered inner-city public schools to be racially desegregated. In many cities, including San Francisco and Boston, whites fled to the suburbs or enrolled their children in parochial or private schools.
Only one in five students in the Boston schools today is white. But many go to private schools until the sixth grade, giving them an advantage city leaders say is not available to poorer black and Hispanic candidates for entry into Boston Latin. The school reserves 850 of its 2,500 seats for blacks and Hispanics; without the quota, only 350 would get in.
Lowell limits Chinese-American enrolment to 40 per cent, and this year rejected 94 Chinese-American students who earned higher scores on the admission tests than youths of other races. Out of a possible top grade of 69, Chinese-Americans had to score at least 63 while whites and other Asians could enter with 60 and Hispanics and blacks with 50.
Such policies are an imperfect solution until a better one can be found, said Suwada Hines, a black 11th grader.
But Matt Freeley, a white classmate, argued: "If you're smarter than somebody, and you score higher than them, you should get in. It shouldn't be because of the colour of your skin."
Lowell this month proposed a compromise under which 80 per cent of entering students would be accepted solely on the basis of their test scores, while the other 20 per cent would be judged by other criteria - including not race, but socio-economic status. The idea remains under consideration by the school board, but is popular.
"Unfortunately, in a democracy, race still matters," Mr Quan said. "We talk about all these quotas in education, but once a person graduates, race becomes important again, no matter what your race. Like any other group, if I'm the one that has the advantage, I think it's great."