For more than a decade, the five men whose convictions were vacated in the 1989 rape and beating of a Central Park jogger grappled with New York City for monetary damages for what they had gone through. The city fought them at every turn.

Then, six months into a new administration, the city’s Law Department agreed to a sweeping $41 million settlement with the plaintiffs. The agreement, which is expected to be filed in federal court soon, had been championed by Mayor Bill de Blasio, who had cited the city’s “moral obligation to respond to that injustice.”

It was the second of several substantial payments in civil-rights cases so far this year. In February, the comptroller’s office agreed to give a Brooklyn man $6.4 million for his erroneous conviction and 23-year prison term for a 1990 murder of a rabbi; the payment came before the man, David Ranta, even filed a lawsuit.

Late last week, the city agreed to pay $2.75 million to settle a lawsuit that had accused correction officers at Rikers Island of the 2012 fatal beating of Ronald Spear, a 52-year-old inmate suffering from kidney disease. The settlement was one of the largest reached by the city in recent years to resolve a case involving violence against a city prisoner.