Instead of popcorn, you can apply a layer of sand-textured paint to the ceiling. It looks a lot nicer than the popcorn and hides surface imperfections pretty well. I did this in my living room because there was a visible seam running across the middle and I sure wasn't going to re-drywall it. The texture really did a good job hiding it. I used this Behr paint
, applied it to the ceiling with a looped texture roller
, then knocked down the peaks with a wide plastic drywall knife. It looks close to the picture below, but I moved the trowel mostly in the same direction, so my ceiling looks a bit less busy than this.