THE POLICEMAN who takes careful aim and brings down an armed bank robber who has just shot a security guard and a teller becomes a hero. A sheriff who wounds and disables a kidnapper threatening the life of a small child is responding just the way the public expects him to. And an FBI agent who kills a terrorist two seconds before he is able to detonate a bomb gets a commendation. We expect lawmen to protect us, and we expect -- even encourage -- them to use deadly force when that is necessary.

By the same token we would be profoundly shocked if trespassers, red-light runners or tax evaders were killed by law-enforcement officers who were seeking to make an arrest. The response is wildly out of line, the magnitude of force entirely unjustified. In real life, though, the choices police face are often not as clear-cut as these examples. Is the burglar wielding a flashlight or a gun? Are there innocent bystanders who might be hit by a stray bullet? Is the 70-year-old drunk waving the knife really capable of hurting anyone? Judgment calls must be made by oficers every day, but those decisions are made more easily if guidelines for using force are clear.

In October 1974, Memphis police officer Elton Hymon shot and killed a burglar fleeing from a house at night. The use of deadly force was, at the time, permitted in Tennessee and a number of other states, because the officer had given warning. The shooting also met a narrower Memphis Police Department test because the crime in question was a felony. It was never clear, though, that the suspect had injured anyone in the house or that he was armed or dangerous. As it turned out, he was a slightly built, unarmed boy of 15 who had stolen $10. The Supreme Court ruled this week that the broad Tennessee statute sanctioning deadly force in a case of this kind is unconstitutional and that use of such force by the police is justified only when the officer has probable cause to believe that the fleeing suspect has seriously harmed or threatens to harm the officer or others.

Most big-city police departments and the FBI already operate under such restrictions and do so without hampering effective law enforcement. Police organizations, some of whom filed friend-of- the-court briefs challenging the statute, have welcomed the court's ruling. They make the point that broad deadly force laws increase tensions between the community and the police and make the job of law enforcement more difficult. Justice White, writing for the majority, acknowledges that some suspected of serious crime will, occasionally and temporarily, escape. But "it is not better," he says, "that all felony suspects die than that they escape." With this sensible and humane decision, the court has wisely reduced the risk of that happening.