You are correct, you will need two different size sockets. I don't remember the sizes off hand but the one size will remove the two with the nipples on to remove your wheel cover and than the other to remove your actual lugnuts. I purchased mine at camping world a bunch of years ago. I only replaced the two because I am assuming the previous owner must have damaged or battered them trying to remove them possibly with the wrong size socket. These don't have to be nearly as tight as the wheel lugs which are torqued at about 450 ft lbs. I removed the small locking nut from the damaged chrome caps and carefully tapped the smaller nuts into the new chrome caps. Good luck, Don
2003 Dolphin Model 5380, Workhorse 8.1, 04 Honda CRV, Brake Buddy, Blue Ox, Banks System, Garmin 7200.