In one case, investigators say 29-year veteran Eddie Polite after photos surfaces showing him asleep in his uniform in his personal vehicle.
Polite was reportedly working an Uptown paid detail at the time, which investigators say he later lied about to superiors.
WWL-TV reports Polite was already under scrutiny for a drunk-driving arrest months ago in Harahan.
Two other officers were today fired over an unrelated incident.
Officials say officers Kevin Wheeler and Juan Vera lied about an incident in which the two cops deployed their tasers on a man.
Both Wheeler and Vera issued statements saying they "tased" an armed man after responding to a call of a man with a machete, according to the NOPD.
However, investigators say all such taser deployments are automatically recorded on video, and the videos showed the man was unarmed and posed "no serious threat of bodily harm to either officer at the time.
Another officer, Larry King, has been suspended for five days for not reporting the alleged misconduct of Wheeler and Vera.
In a written statement, NOPD Superintendent Ronal Serpas said he is also concerned that the investigation into the two officers' alleged misconduct is not over.
“In the Wheeler and Vera case, I am very satisfied that our internal control systems determined that the information provided in the police report did not match evidence available. I applaud their integrity, and am confident in their abilities as leaders; however, what is disappointing is that on-scene supervision failed and we have initiated an investigation into potential serious violations by field supervisors,” Serpas said.