CLAREMONT, N.H. — It's a new riff in the hour-long stump speech of Sen. Bernie Sanders (I-Vt.) -- a slow burn. It begins with some ruminations about how "people would have thought you were crazy" if you said the United States in 2015 would have a black president. That's good, Sanders says — everybody give a pat on the back — but it shouldn't end the conversation.

"When I mention a few names, like Sandra Bland or Michael Brown or Rekia Boyd or Eric Garner or Walter Scott or Freddie Gray or Tamir Rice or recently Samuel DuBose, you know and I know that unarmed African Americans have been shot and killed by police forces in a way that never would have happened if they were white," Sanders, who is seeking the Democratic presidential nomination, said at a campaign stop in Franklin, one of  half a dozen appearances this weekend in the first primary state. "We need to move away from the militarization of the police forces."

In Franklin, a crowd of hundreds that included no black faces broke into cheers and applause. A crowd in Claremont, mostly white, cheered inside and outside the Common Man Tavern, where Sanders was speaking. "This audience is more lily white than an albino eating a powdered doughnut in a storm," joked Rod Webber, a flower-bearing political tourist and filmmaker who said he was not impressed by the way Sanders talked about race.

Two weeks had passed since Black Lives Matter protesters crashed Sanders's speech at a progressive conference. They demanded that he stop talking generally about economic issues, stop talking about his role in the civil rights movement of the 1960s, and say the names of black people killed by police. In their view, he whiffed — and that was before he skipped a meeting with organizers and sent his campaign manager as a ringer.

Sanders and his campaign learned quickly, and reached out to Black Lives Matter activists for insight on police reform. A week ago, the candidate gave the Southern Christian Leadership Conference his take on the death of Sandra Bland, and came out for mandatory body cameras on police officers. On Friday, when he addressed the national conference of the Urban League, Sanders rattled off the names of Brand, Brown, Boyd, Garner, Scott, Gray and Rice and presented his own changed standards. "Violence and brutality of any kind, particularly at the hands of law enforcement sworn to protect and serve their communities, is unacceptable and must not be tolerated, he said. "We must reform our criminal justice system. Black lives do matter, and we must value black lives."

Over a long weekend of campaign stops in New Hampshire, Sanders honed that message. "Police in Ferguson looked like an invading army," Sanders said in Franklin, referring to Ferguson, Mo., where Brown was killed. "I was a mayor for eight years, and I know police a little bit. It's a very difficult job they've got. But when we do it the best way, we have community policing. Police are part of the community. They are not seen as oppressors."

He was no longer speaking to black activists, although he may as well have been. He was talking to white progressives, who had been horrified by the same police stories.

"What happened in Texas with Sandra Bland was just insane," said Howard Moffett, a 71-year-old Democratic state legislator, who came to the rally with a bookmarked copy of Ta-Nehisi Coates's bestselling book "Between the World and Me." "I had questions about whether it was a good idea to have body cameras on cops. No more. I'm sold on them. I think we need them, and I think that cops that are not properly trained should not be let loose on the public," he said.

In Claremont, a town close to the Vermont border that has a 94 percent white population, Sanders concluded his campaign swing with an even starker version of the pitch.

"You know these names," he said. "You know these names because some of these people were murdered by police officers. And they would not have been murdered if they were white."