The legal front widening against makers of opioid painkillers has something in common with landmark tobacco litigation of the 1990s: attorney Mike Moore.

As Mississippi’s attorney general in 1994, Mr. Moore filed the first state lawsuit against tobacco companies, saying they harmed public-health systems by misrepresenting smoking’s dangers. He helped marshal the subsequent spate of state litigation and then the talks that led to a $246 billion settlement.

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