Fighting crime in New York City—like in any large metropolis—comes with many challenges. There are more than eight million residents in the five boroughs, and many hundreds of thousands more people travel to and through the city each day. In contrast, the police department employs only about thirty-four thousand uniformed officers. A department so outnumbered is bound to make mistakes—crimes go unsolved, innocent people are falsely accused, criminals remain unpunished.

And while many New Yorkers conduct their days without interference from police officers, the relationship between law enforcement and communities that the N.Y.P.D. has determined contain high concentrations of crime—thus requiring a heightened police presence—is a complicated, quarrelsome one. In Brooklyn’s East Flatbush neighborhood, demonstrations that have been alternately prayerful and violent continue two weeks after two officers fatally shot sixteen-year-old Kimani Gray, who they contend drew his gun first. While the investigation into Gray’s killing continues, and while his family and the community work through their grief, the policy that arguably led indirectly to his death—a policy that Police Commissioner Raymond Kelly and Mayor Michael Bloomberg have vigorously enforced and defended—is facing a serious challenge in court.

The plaintiffs in Floyd v. City of New York, a class-action lawsuit regarding the N.Y.P.D.’s stop-and-frisk practices that went to trial last week, contend that stop-and-frisk practices violate the Fourth Amendment’s prohibition against unreasonable searches and seizures and the Equal Protection Clause of the Fourteenth Amendment. But that’s the legal wording. In a press briefing a few days before the trial began, David Ourlicht, one of the four named plaintiffs, put the violations he feels into more everyday terms:

I don’t [want to] have to walk outside and have that thought in the back of my mind: “This time will they shoot me or will I get beat up? Will I go to jail for something I didn’t do?” I want to be able to move on and not have to feel that. I don’t want my friends to have to feel that anymore. I don’t want my—when I have kids, I don’t want them to feel that.

American history brims with reasons why some citizens must fight harder than others to have a fair shot: economic inequality, political maneuvering, unfair policies, simple and single-minded discrimination. Thankfully, there are also stories of redress in our past. The Floyd case may never reach the stature of 1954’s Brown v. Board of Education, but if the plaintiffs are successful, it would be a major step in addressing all-too-legitimate grievances that minority communities have against big-city law-enforcement agencies. Perhaps the most striking feature of this case is that, unlike other attempts to end discriminatory policing through the court system, Floyd stands a good chance of succeeding.

In two rulings issued last May, Federal District Court Judge Shira Scheindlin moved the case beyond the point at which racial-profiling claims like this one typically get stalled. To get any lawsuit heard in court, a plaintiff must establish that they have standing—that is, they must show that they have suffered an actual injury, whether physical, mental, financial, or otherwise. If the plaintiffs in this case had been seeking only monetary damages, ordinary standing would have been enough. But in a 1982 case, Los Angeles v. Lyons, the Supreme Court set a higher standard for anyone who sought to use the court system to force a change in police tactics. That case focussed on a man named Adolph Lyons, who was stopped for a traffic violation by officers who, without provocation, put him in a choke-hold. In its decision, the Court said that Lyons could sue for financial compensation but that he did not have standing to seek an injunction that would force L.A.’s police to stop using the hold, and that in order to establish standing, he’d have to “establish a real and immediate threat” that the same thing would happen again—not just to anyone, but to him specifically. It’s on these grounds that other, similar suits have failed, and New York tried to bring Floyd to an end in the same way. But stop-and-frisk is different: because it is so pervasive in areas of the city, so likely to happen to those who look a certain way, the program itself may end up being its own undoing. “The simplest way to address the defendants’ concern [about standing],” Scheindlin wrote in her ruling, “is by noting that David Ourlicht, the fourth plaintiff, indisputably does have standing…” as he was stopped “three times in 2008 and once again in 2010, after this lawsuit was filed.” Moreover, as Scheindlin continued, “the police department has conducted over 2.8 million stops over six years and its paperwork indicates that, at the very least, 60,000 of the stops were unconstitutional (because they were based on nothing more than a person’s ‘furtive movement’).” (The italics are Scheindlin’s.) And because Scheindlin saw Ourlicht as having standing, all the other plaintiffs—named and unnamed—automatically have it as well, as part of the class bringing the lawsuit.

The city argues that, despite these figures—and in contrast to data that the plaintiffs’ attorneys will present about the discriminatory effect of stop-and-frisk—there is not enough of a “disparate impact” on minority communities to constitute a “discriminatory purpose.” It will say that the N.Y.P.D. justifiably sends more personnel into black and Latino neighborhoods, that the officers go where the crime is. And it will point to the “Stop, Question and Frisk Report Worksheet,” which officers are required to fill out after they stop someone, as a way of legitimizing their actions—and hedge against any claim of unlawful racial profiling. The forms include choices like “fits description,” “furtive movements,” and “wearing clothes/disguises commonly used in commission of crime” as reasons for a stop.

Justifications like these have been enough for a court to consider a stop constitutionally permissible, even if the real motivation was race, based on a precedent set in a 1996 Supreme Court decision. The Court took up a case in which Michael Whren and James Brown claimed unreasonable search and seizure during a traffic stop by Washington, D.C., officers. When the two were stopped for a legitimate traffic violation, one of the officers saw that Whren was in possession of crack cocaine, resulting in federal drug charges for the two. The legal dispute arose when the plaintiffs contended that the officers used the traffic violation as a pretext to conduct a search motivated by race. The Court unanimously ruled the search permissible, saying that, because the officers had probable cause to stop Whren and Brown, their reasons for doing so did not matter. Writing for the Court, Justice Scalia said, “the Fourth Amendment’s concern with ‘reasonableness’ allows certain actions to be taken in certain circumstances, whatever the subjective intent.” (Italics in the original.) In New York City, the combination of the Whren decision and the justifications for stop-and-frisk encouraged by the N.Y.P.D. has left communities with legitimate suspicions of and reasons to fear law enforcement less protected, not more. Floyd might be a step toward addressing that, toward resetting the balance of power between citizens and the police who are supposed to serve them.