Furniture, Wood and Cabinetry Finishing - Rust rings in table top

I have a veneered chairside radio that was used to store paint cans on. The top has several rings on it, some parts of the ring stained by rust. I have used Parks wood bleach several times. The veneer now is pretty white, but the rings can still be seen, even whiter. I got it as good as I could, then stained. The rings popped back out as bad as they ever where. This thing looks impossible, but is there something else to try? Thanks, Ken, Roanoke, Va.

Ken:

Assuming the piece has stain only (no finish), here's something else you can try - no guarantees.

Scrub the top with a paste made of baking soda and water using a damp sponge. This will lighten the wood some, but it should attack the stain even more so. After cleaning off the residue, use a wood conditioner on the top before restaining - this helps even out the absorpotion of the stain.

After trying the above (baking soda) wipe the piece down with a rag wet with lacquer thinner. The look of the piece while wet will let you know how much of the stain is still there - hopefully it won't be much.