I've got an old LCP that has never jammed with FMJ, HP's or reloads. Makes a dandy summer gun and disappears in cargo shorts.
I hadn't shot it in 3-4 months so I took it out this afternoon. I just treat it like a DAO revolver, block the slide over whatever I want to hit and stroke the trigger quick and straight back. I shot both magazines empty on 6" plates at 7 yards and an 11x17 plate at 25. No misses and no jams- about all you can ask of a pocket gun.
The little pistol feeds anything but I carry FMJ in it. In that caliber you don't have any penetration to spare. You need all you can get.