The new strategy has had the effect of excluding the de Blasio administration from the settlement process in several high-profile cases. But Mr. Stringer, who as comptroller is the steward of the city’s investments and finances, made it clear that he is trying to strike a fair agreement where his office finds that claims have merit.

Mr. Stringer, alluding to Mr. Thompson’s review, added, “I am aware that we do have the potential for these cases coming to us over the next couple of years.”

In a statement, Nicholas Paolucci, a spokesman for the Law Department, said that such settlements are within the comptroller’s authority. “Particularly in a case in which a district attorney has made an independent assessment that a criminal conviction should be vacated, an early resolution can be prudent and fair.”

The settlements announced on Sunday will pay $7.15 million to Mr. Hill, who spent about 27 years in prison until his release last year; $6 million to Mr. Jennette, who was released on parole in 2007 after about 20 years in prison; and $3.85 million to the estate of Mr. Austin, who died in prison in 2000 after 13 years there.

Mr. Hill and Mr. Jennette, who were incarcerated in other prisons, learned of their brother’s death through the mail. Louise Austin, a pastor in North Carolina — and the mother of all three men — stood in for Mr. Austin at the hearing in May when his conviction was vacated.

Pierre Sussman, the brothers’ lawyer, said that the quick resolution was in everyone’s best interest — the two surviving brothers are in their 50s, he said, and Mr. Hill has multiple sclerosis — and avoids potentially years of litigation. “They had no interest in going through that lengthy process,” he said.

Mr. Sussman, who had also represented Mr. Ranta, said the brothers’ settlements are higher per year than some of the wrongful-conviction cases that had been pursued in court. “That speaks to the strength of these cases, and that may be the Scarcella factor at work,” he said.