When Education Secretary William Bennett talks about "choice," you can almost see his mental flashbacks to his days at Gonzaga, the highly regarded Catholic boys' school here.

What you are hearing is not simply a pitch for tuition tax credits, though he certainly supports that idea. Bennett's sincerity is unmistakable when he says he wants for your children what Gonzaga afforded him: Not necessarily a Catholic education, but choice.

If he had his way, he acknowledged over lunch in his office dining room, the schools attended by most of our children "would not be public except in the trivial sense of being supported by public funds. In all other ways, they would tend to operate like private schools."

He'd have an end to dictatorial central offices, spewing regulations calculated to make every school an unimaginative replica of every other school. He'd give parents a choice.

"What is distinctive about private school? It is distinctive. It has a character. Let's let public schools have a character. How do we let them have a character? Good leaders, that's what we're talking about; more involvement with parents; changing the structures so that the public schools will have the power to develop the kinds of features that make private schools distinctive and successful."

Choice of the sort Bennett has in mind would work wonders. It would improve the curriculum, it would increase parental involvement, and it would increase achievement. Schools would either succeed or perish.

I listen to Bennett and I try to think of the good schools I know. Some are good because, as private enterprises, they are free to exclude the children who don't fit their conception of what their pupils ought to be. The exclusions can be based on anything from IQ to social class to gender. In other words, the choice Bennett touts may belong more to schools than to parents.

The schools that fascinate are those that are able to achieve excellence without being exclusive: the public schools, often in unlikely neighborhoods, that regularly turn out winners.

Bennett knows about these schools, and he knows, too, that the one thing they have in common is that they are run by extraordinary principals, often in quiet defiance of central-office guidelines.

But Bennett (so it seems to me) extracts wrong lessons. First, he assumes that, because the role of the principal is crucial, the way to replicate these oases of learning is to give parents the right to select their own principals, without being limited to those people in the system who have "had their tickets punched." Second, he assumes that, because strong and successful principals tend to follow their own dictates rather than those of the central office, the way to increase the number of good schools is to weaken the control of the central office.

I agree that parents ought to have a major role in selecting their principals -- as, in fact, they do in the more affluent neighborhoods. But however attractive it sounds to be free to choose anybody -- including people without experience either as teachers or as administrators -- the people who have the skills and desire to be principals are likely to be those who, in one way or another, have already started getting their tickets punched.

As for the dead, unimaginative hand of "downtown," it's a fair bet that more schools would be hurt than helped by eliminating the control of the central office. The outstanding principals know how to work around that control; the mediocre principals may need it.

The schools least likely to benefit from the "choice" Bennett has in mind are precisely those schools that most need improvement, and the likely result would be a widening of the gap between those schools that serve the rich and those that serve the poor. The former would get virtually everything they wanted, while the latter would lose even the support of the central office.