Slim toilet tank?

We want to put bead board wainscotting in our powder room. We are planning to replace the toilet. The current toilet seems to be a smaller than normal size, but it does have 12" from the bolts to the back wall. The tank butts directly to the back wall now, so are there any slimmer tanks that would sit further from the wall (and allow the wainscotting to fit behind the toilet?) I do not want to move the hole, for two reasons: the space is already tight, and I do not want to go to the expense of having the whole relocated.
Thanks

tanks

Any slimmer tank would have to be from the same manufacturer and also be compatible with your toilet. Normally the answer would be NO.

Often toilets that are classified as a 12" rough in actually only take about 11-1/2 or so. I am thinking specifically of the Toto Drake, but there are others. This would be an excellent excuse of getting a 21st century toilet. Check to see if there are rebates available in your area for making the switch.

Most new toilets will work at 11-1/4"