I smoked a bone-in back strap on Sunday. It turned out pretty good. I injected it with some butter with garlic, salt and pepper, and coated it in butter. I smoked it with bacon over the top of the back strap. I smoked it at about 250-275 degrees for about 2+ hours. I pulled it off once the internal temp was at 135 and 138 degrees in multiple spots in the meat. I let it rest in a cooler for about 30 minutes while we were cooking other items for dinner. It turned out very nice. My wife and daughter still like back strap steaks better, but I thought it was pretty good.
I recently tried the backstrap bone in, but with the tenders, too...my buddy calls it "the saddle".
Mesquite smoked for 2.5 hours and and then in venison/ham broth overnight on low in the oven. Oven was old and the lowest oven setting was a bit too high. Cooked it a little more than I wanted it. But still tasty.