City lawyers have agreed to pay $1.6 million to the family of Alberta Spruill, a 57-year-old Harlem woman who died after the police threw a stun grenade into her apartment during a mistaken raid, officials said late yesterday.

The settlement was notable not so much for the amount as for the speed with which it was reached. It came a mere five and a half months after Ms. Spruill, a longtime city employee, died of a heart attack induced by the use of the grenade in a no-knock raid on her apartment, which the police had been told was used by a drug dealer. At the time, the drug dealer was already in custody.

Derek S. Sells, a lawyer for the Spruill family, declined to comment on the settlement.

City officials suggested that the speed of the settlement showed Mayor Michael R. Bloomberg's determination to lower legal costs and speed up the resolution of cases.

Settlements in wrongful death cases usually do not come until after preliminary proceedings, like the taking of depositions, a process that takes about two years, said Sanford Rubenstein, a lawyer who has represented plaintiffs in several such cases. ''I think it's a signal perhaps that the city is doing the right thing where it's appropriate,'' he said.