Can the NYPD dial down its traditional tough-cop culture and morph into a new kind of agency that keeps crime low while winning the trust and respect of 8.4 million New Yorkers? It has no choice.

Protesters have pounded home a painful lesson for America's largest cop shop: It's not enough to send crime rates into free-fall. If the people the NYPD polices see cops as chronically nasty and brutal, the cops can expect some pushback.

That helps explain the furious reaction last week after a Staten Island grand jury declined to indict Officer Daniel Pantaleo in the death of Eric Garner -- a death seen worldwide in a viral cellphone video.

So now Mayor Bill de Blasio and NYPD Commissioner Bill Bratton have started a retraining program for around 22,000 officers. Oddly, the force has done little in-service training over the years.

Outdated ideas of policing have persisted for way too long.

What should improve? Start with this:

Takedowns. The NYPD must teach cops new ways to control tense situations -- minimizing physical danger to officers and to subjects. The de-escalation of ugly language is one technique. Trying harder to wear down a resistant subject with words instead of physical force is another. Demeanor. Body cameras on officers should make a real difference. A camera will not settle every dispute. But it should settle many. And cameras should keep cops and citizens on their best behavior -- preventing new Garner-type scenarios. Respect.After rookie cop Peter Liang fired a bullet that struck Akai Gurley in a Brooklyn stairwell last month, he texted his union rep instead of seeking help for the dying man, the New York Daily News reported Friday. That's a shocker, and it hardly speaks well of Liang's training.

Discipline. Problem cops implicated in brutality cases often have records of frequent citizen complaints or lawsuits. The NYPD should monitor these signals more carefully and fire bad apples sooner.

The task ahead will pose a major test of Bratton's skills. Police union president Pat Lynch is already claiming de Blasio has tossed cops "under the bus." That's wrong. The city wants to make cops and citizens safer and the city more civil. This is a challenge we can't afford to lose.