The law (and common sense) says we need clearance from combustables. One way to legally be close to a combustable is to make a heat shield. You can make one quite easily. It isn't much money, and very safe. Get a sheet of aluminum, .04" is fine, even a bit thinner is OK, but the thinner stuff gets bent easily. Using 1/2" copper tubing, cut a bunch of one inch pieces. Cut the aluminum so it covers the wall that needs protecting. Whatever you need for clearance, make it so that after it is installed you have the proper distance from any part of the stove to any combustable. Find where the studs are in the wall ( a magnet will find screws or nails telling there's a stud there). Drill holes in the aluminum so they line up with the studs. Before drilling, you need to know one thing: The alumium must be one inch off the floor when you are done. That is what makes the shield work.... air gets drawn up from the bottom, making a chimney of sorts. It's this moving air that keeps the wall cool. Using sheet rock screws, go through the aluminum, through one of the copper spacers and into the stud. At least four spacers per sheet of aluminum, use your own judgement. At a corner, the aluminum stops an inch from the wall. The aluminum on the other wall meets it in mid air.
Don't forget to do behind the stove pipe if it is a bare pipe. Another way to do stove pipe is, if it's a 6" pipe, use 8" and screw it to the 6" so it makes a one inch space all around.
Note: Bricks ON a wall do not protect it from heat. ANY shield needs air space behind it and a way for that air to move. The only reason bricks or slate on a floor are OK is that heat rises.
I just checked with the fire chief. A heat shield provides a 50% reduction. Like: a soid fual appliance needs 36" clearance, with a heat shied you can go 18". He said you can get down to nine inches if you build a non cumbustable wall THAT IS SPACED from the combustable wall. This can be made of brick or two layers of gypsom board. The last thing he said was to check with your local fire department. Different states have different laws, and even some cities have tighter laws.