Valve Shim Met it's Limit

Here's a good one. I check the valves, which this is the second time since I've owned my 2k 4cyl with 317 miles. Last time I had to pull the head since I let one get to tight and burned and exhaust. So now my tightest one has .007 clearance out of a .011-.015 limit on the exhaust. My shim is a 2.50 which is the thinnest one they make. I need a 2.40 and that's putting it on the low side, but would like a 2.35. So with a 2.50 being the thinnest, and short of a machine shop maybe milling it down some, and taking a, I'll say slim chance of it deforming the shim when I put it back in, does anyone have any suggestions??

I would take the thinnest shim and rub it in a circular motion on fine (1500?) emery or croccus cloth held flat on an anvil or piece of glass. Check the thickness every so often, more frequently at first, then as often as you feel comfortable. Be careful that the edges of the shim don't get worn by you pressing off-center or the emery cloth bunching up in front of the direction your pushing the shim.

After the center is the thickness you want, check in other spots at the midpoint between the center and edges. I would be satisfied if the micrometer only measured differences of 0.01. After you get the thickness you want, polish it with a metal polish and cloth.

Was thinking about that but these shims seem to be made out of some tough stuff. Afraid that using Emory cloth might take me a year (haha) to do it.😝 I'll post what I end up doing.

If the going is too slow, use a coarser grade (600?) to take off the first 75% of the thickness. Graduate to fine cloth once you are near your target. Don't hurry. Hurry will make garbage.