I was trying to swap my spare tire in for one of the wheels to help track down a vibration/balance problem I've been having, but I can't seem to get the wheel nuts loose. They seem to be kind of loose (I guess they have some sort of chromey cap on them)? How the heck are you supposed to break them loose if the socket just slides off them?

 

sounds like you have "locking" wheels nuts any chance of a picture so I have an idea and can hopefully suggest removal method if you don't have the "key"?
all the non key methods I know are a destructive though!

 

Jag had a problem at one time with the in-trunk
supplied wheel wrench that was not sized and hardened correctly and could chew up lug nuts.
Make sure you use a 11 mm socket.

 

It can't be a key, the tire shop was able to get them off no questions asked a few months ago!

They just look like standard lug nuts with kind of loose "caps". Chromey! No crazy shape or pattern!

BTW there is no way it's an 11mm socket. Maybe 22!

 

Woops...!
I am talking about the lug nut thread size not the width across the flats of the wrench to pull it off, which as you say is closer to 3/4 inch.
This should help....
The lug bolt/nut thread size is 12 x 1.5 ( metric), there are other threads on this forum about the cap stripping problem.
Some ppl choose not to pay the @@20.00 per that Jag charge and match up at parts stores or buy from Toyota dealer, or here are more tips
Wow, Chysler Sebring parts for a Jag...LOL!
That ebay set looks a deal ... a complete set for the price of one oem.
It is funny cuz I have that same little "ker-ching " noise at slow speed , it took me for ever to see it was the caps rattling on some the nuts.There was an older long term road test in a car mag that said they had that same problem whilst trying to change a tire in the rain, ended up getting the car towed.

https://www.jaguarforums.com/forum/s...ug-nuts-32510/

http://www.whtknight.com/2009-05-18%20applicationB.pdf

PS, mine are pretty chewed up with all the off and ons with my brake issues, cannot really fault the ppl that worked on the car as it really is a crappy design, I also noticed when I changed a flat on the side of the road how heavy the damned thing is and how hard to line up and get started, some shops often seem to chip paint off if they try and run the nuts on with air tools instead of starting by hand.
Oh, can any one get the spare wheel hatch cover to stay clipped on the trunk molding via the handle like it is supposed to, mine does it for a minute then falls on my head.