Mayor Bill de Blasio and the United Federation of Teachers are fine-tuning a push to water down the supertough admissions exam for New York's eight top-rated, elite public high schools.

That's the wrong answer. While the admissions process needs remedial work, it should stay as rigorous as ever.

De Blasio is right about the problem. While our society is supposed to be based on fairness, he says, the specialized schools don't reflect "the kind of fairness that any New Yorker would recognize."

Here is what he's talking about.

Hispanics are 40% of the school system's enrollment, blacks are 28% and Asians and whites are 15% each. Yet of the 3,292 students admitted to prestigious Stuyvesant High School this year, 73% are Asian and 22% are white. Just 2% are Hispanic and 1% are black.

But the mayor flunks completely when it comes to a solution.

His new Specialized High School Admissions Test might offer exam graders leeway -- incorporating essay questions, for example, that would let them subjectively give students the benefit of the doubt.

Instead, the city should do more to identify and encourage promising black and Hispanic students who have the potential to succeed. Here are some ways:

Seek some diamonds in the rough. The city should pay particular attention to middle schoolers who are stars but fall just short on the specialized admissions test. A mechanism to allow some admission -- with an authoritative recommendation from a principal, say -- could make a big difference. This strategy might require a change in state law that now makes the test the sole criterion for the city's three original selective high schools -- Stuyvesant, Bronx Science and Brooklyn Tech.

Grow the pie.There are only eight selective schools. Mayor Michael Bloomberg created five. De Blasio should follow his lead and create more.

Tutoring, tutoring, tutoring. Enlist foundations and other private groups to the cause. Not all minority students can afford pricey test-preparation services. Tutors who understand the admissions drill could prove indispensable.

Support charter schools. The best ones put a heavy emphasis on academic excellence. And many have seen stunning success in black and Hispanic neighborhoods. If more come on line, they could be key feeders into selective high schools. Unfortunately, de Blasio isn't a fan.

Every promising kid should get a shot.