Tuesday night, PBS aired a remarkable documentary about a criminal justice experiment in a crime-plagued neighborhood in Brooklyn, New York.”Red Hook Justice” is the story of the Red Hook Community Justice Center, a neighborhood-based court that is testing a new response to low-level criminal behavior like drug possession, prostitution, and vandalism.

Instead of sentencing offenders to short-term jail (or, worse, to nothing at all),the Justice Center combines punishment and help, mandating low-level miscreants to perform community service and receive the kinds of services – drug treatment, job training, mental-health counseling – that might, with a little bit of luck, help them avoid coming back to court again.

What does this look like in practice? In “Red Hook Justice,” we meet Anthony, a teenager with a propensity for misbehavior who is linked to a dizzying array of services, including job training and life-skills classes. We meet Michael, who is busted for marijuana and given a chance to avoid both jail and a criminal record if he successfully completes community service. And we meet Letitia, a drug-addicted former prostitute who attempts to wrestle her drug habit under control with the help of court ordered drug treatment.

Presiding over the whole enterprise is Judge Alex Calabrese, who ensures accountability by requiring offenders to return to court on a regular basis to report on their compliance with his orders. Judge Calabrese espouses a concept known as “problem-solving justice.” Problem solving justice is the idea that courts should do more than just process cases like widgets in a factory. Rather, they should affirmatively seek to address the problems of defendants, victims, and communities. According to Judge Calabrese, “As a judge in a traditional court, I felt like an artist with two colors: in jail or out of jail. At the Justice Center, I have the tools to give people the opportunity to change their lives.”

Problem-solving judges like Calabrese recognize that today’s criminal courts bear little resemblance to the courts we read about in our grade-school civics classes. Spend a few hours watching Court TV or “Law and Order” and you’d think that the typical criminal case is a serious felony involving a hardened criminal, a celebrity, or both. In real life, the typical criminal is a petty offender suffering from addiction, mental illness, or homelessness. Moreover, rather than hard-fought trials where prosecutors and defense attorneys go head-to-head, the vast majority of cases in American courts are resolved by plea bargain.

New York State Chief Judge Judith S. Kaye explains the problem this way: “In many of today’s cases, the traditional approach yields unsatisfying results. The addict arrested for drug dealing is adjudicated, does time, then goes right back to dealing on the street. Every legal right is protected, all procedures are followed, yet we aren’t making a dent in the underlying problem. Not good for the parties involved. Not good for the community. Not good for the courts.” Put simply, there’s not much to recommend about business as usual in many American criminal courts.

That’s why experiments like the one in Red Hook are so important. The Red Hook project is still in its early stages, but already it has achieved some promising results. Public confidence in justice is up, as are property values. Levels of fear are down along with crime rates. For the first time in more than a generation, Red Hook recently went an entire calendar year without a single homicide.

While the Red Hook project has received the most attention, it is hardly the only one of its kind. Indeed, three dozen American cities are adapting elements of the Red Hook model. Even the Blair government in Great Britain has gotten into the act, launching a community court of their own in Liverpool.

Will the innovations being tested in these cities transform the way that all courts work? It is too soon to tell. But these projects do offer a beacon of hope for those of us who care about justice. Coming off an era when the conventional wisdom was that “nothing works,” that it is impossible to change the behavior of offenders, this is good news indeed.

Mr. Berman is co-author of “Good Courts: The Case for Problem-Solving Justice” (The New Press) and the director of the Center for Court Innovation, a think tank that promotes new thinking about how courts can improve public confidence in justice.