With due respect to the most famous Irish family in American politics, one of the Kennedy legacies could be laid to rest soon. That is the “diversity visa” program established decades ago by the late U.S. Sen. Ted Kennedy, D-Mass., who wanted to take special care of the Emerald Isle.

The program allows 50,000 green cards for permanent residency in the United States via a lottery.

Unlike other programs that allow temporary visas for highly qualified workers, the program is for good; it also is intended to provide a route to residency from countries “under-represented” in the other immigration programs.

For Kennedy and others fond of Ireland, those included many people who had overstayed their visas.

As few Irish emigrate from their homeland to America now, compared with the days when the original Kennedys came over, it was a real help to those constituents in Boston and elsewhere.

And when Kennedy originally put it into law, it took particular care to count Ireland and Northern Ireland as separate countries in the lottery’s quota system.

Over time, the program has benefited immigrants from Africa as much as from Europe and Asia, but it’s still the only way to get a green card with only a high-school education, writes Peter Schuck, a Yale Law School professor, in The Los Angeles Times.

Schuck argued that its provisions ought to be focused on people with substantial skills instead of a pure lottery. It is a good point, and Kennedy himself was familiar with Canada’s system, in which residency can be “bought” with investments in Canadian business or with advanced degrees or other skills.

Schuck is hardly anti-immigrant: “Immigration is in many ways the lifeblood, future and salvation of an aging, technology-driven America,” he wrote. “The stakes could hardly be higher in getting our immigration policy right and bringing in those who can provide what we need: skills, entrepreneurs, close family members and investment.”

The legacy of the Kennedys is a splendid one in this country, but we agree that this policy could use some tweaking, at the least. It would be a way to focus more constructively on immigration policy.