Call them the Willie Hortons of New York. Horton, readers of a certain age may recall, was the convicted murderer who, while free under a furlough program from a prison in Governor Dukakis’s Massachusetts, raped a Maryland woman. Albert Gore, then a senator, raised the issue against Mr. Dukakis in the 1988 Democratic primary. Later, come the general election, George H.W. Bush, then vice president, benefited from campaign commercials using the case to depict Mr. Dukakis as soft on crime. The commercials were accused of having racist overtones, but they made a substantive point about crime and punishment — when someone has committed a serious crime, it’s foolish to let them out on the street again too soon, because there is a risk that they will do it again.

The headlines in New York lately have been full of Willie Horton-like instances of recidivism. The latest and most glaring example is that of a suspect named by police in the shootings of two policemen in Brooklyn on Monday, Dexter Bostic, who was out on parole. That is a problem with parole. Some people let out on parole will shoot policemen, which, if they had been in prison, they wouldn’t be able to do.

But it isn’t just Bostic. A man who was arrested in 2006 for shooting a police officer in the leg after robbing a Queens bank, Joseph Pennington, served three years of a three- to nine-year sentence for grand larceny and possession of a weapon in Queens in 1990 and 1991. Four months after he left prison, he was arrested and convicted of armed robbery, and served 11 and a half years of a six- to 12-year sentence, after which he was let free, allegedly to rob the bank and shoot the police officer. And also last year, there was Darryl Littlejohn, who was sentenced in 1985, 1987, 1992, and 1994 before he was arrested and charged with the murder of a 24-year-old student he met at a Manhattan bar where he was working at a bouncer.

President Bush and others have proposed to invest more in prisoner re-entry programs so that those let out of jail are helped back into society without returning to lives of crime. That’s a fine idea. So are laws that would keep repeat offenders permanently off the streets. Mayor Bloomberg’s reflex is to call for increased gun control. There’s no question that strict enforcement of the state laws against possession of guns by convicted felons is in order. It is, however, but one of many aspects of a policy response to the police shooting, of which a part must be making sure that dangerous, violent, repeat offender criminals are locked up rather than loose on parole where they are free to strike again, as Willie Horton did on furlough.