Once in a yellow moon with green stripes and purple polka dots, the divided capital of this divided country finds an issue on which it is possible, weirdly, to agree.

This summer, the United States will learn whether the overhaul of its criminal-justice system, which locks up more people than any other country’s, is such a moon.

In recent decades, a bipartisan coalition committed to a “war on drugs” and a “tough on crime” stance after the upheavals of the 1960s and ’70s led to a much harsher approach to American punishment — from mandatory-minimum sentences for minor drug offenses to three-strikes laws that imposed automatic life terms on repeat offenders. The ranks of the incarcerated more than quadrupled, to 2.3 million in 2013 from 500,000 in 1980: about 25 percent of the world’s prisoners, in a country with 5 percent of the world’s people.

But today a new coalition is forming, grouping people like President Obama and the billionaire Koch brothers. They are united in the belief that overincarceration has proven ineffectual, wasteful and counterproductive.

The Justice Department is nudging prosecutors to go easier on the drug trade’s small players. The Koch brothers are pushing to end a requirement that job applicants reveal past convictions. There are proposals in the Senate to create a commission on justice reform and to require the police to wear body cameras. But the most advanced effort to change the underlying laws has sprouted in the House, from Robert C. Scott, Democrat of Virginia, and Jim Sensenbrenner, Republican of Wisconsin. Mr. Scott, who has long criticized “overcriminalization,” is the second African-American ever elected to Congress from Virginia. Mr. Sensenbrenner is a strong supporter of mandatory minimums. Yet they have collaborated on legislation, to be introduced this month after incorporating feedback from the Obama administration, that would inject a major dose of mercy into the justice system.

Their bill would sentence most first-time, low-level, nonviolent drug offenders to probation rather than prison; give judges more discretion to grant leniency; create alternatives to prison, like drug-treatment and mental-health programs; reward prison contractors for reducing recidivism; largely end federal prosecution of simple drug possession; and confine mandatory-minimum sentences to high-level traffickers.

In a joint interview last week, I asked Mr. Sensenbrenner about his evolution. And he gave a frighteningly honest response for a man who has sat for decades on the House Judiciary Committee: “We really aren’t exposed to the practical aspect of the criminal-justice system, or what happens or doesn’t happen in the prisons.” So when he and Mr. Scott held hearings on the subject beginning in 2013, Mr. Sensenbrenner said, he got an “education.”

Part of what binds this delicate coalition is the careful elevation of “inefficacy” over “injustice” in criticism of the system. The focus on wastefulness and recidivism has attracted new support from the right.

What neither legislator wanted to discuss were arguments by scholars like Michelle Alexander, author of “The New Jim Crow: Mass Incarceration in the Age of Colorblindness,” that the prison system has served as a de facto regime of racial segregation. Some 40 percent of America’s prisoners are black, roughly three times their societal representation. Mr. Scott said in the interview, “I don’t know why you would get into a debate on racial philosophy.”

The legislators’ praise for their own handiwork consisted of repeatedly calling it “evidence-based,” rather than just, right or moral. Which prompted a question: “Isn’t all legislation evidence-based?”

They laughed. Mr. Sensenbrenner said, “No! No! No!” Especially not with criminal-justice bills, Mr. Scott added, recalling the adage “No politician ever votes against a crime bill named after somebody” — meaning a victim. Now America will learn whether a nameless crime bill, defending faceless and unpopular prisoners, is a rare moon with a chance.

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