Three retired police officers and a former Brooklyn prosecutor were charged on Tuesday in a widening federal corruption investigation into the New York Police Department and its gun-licensing division.

The charges revolve around a scheme in which so-called gun-licensing expediters bribed police officers in exchange for approval of hard-to-obtain gun permits, according to two criminal complaints unsealed on Tuesday in Federal District Court in Manhattan.

The complaints show that a former New York police sergeant, David Villanueva, and Frank Soohoo, a gun-license expediter who dealt frequently with the department’s license division, have pleaded guilty to bribery and other charges and are cooperating with the authorities.

Prosecutors have already said another former officer, Richard Ochetal, who worked in the licensing division for about five years, pleaded guilty and was also assisting investigators.