I bought a 64 Fury with a rebuilt 361 (less than 50 miles on rebuild) about 8 years ago. With the car I got the receipts for the rebuild that totaled $1200.
The engine ran like crap, so I did a compression test and found 2 dead cylinders on opposite sides. I pulled one head expecting to find a burnt valve, but the head looked fine. I ended up installing shims, and it ran excellent after my bandaid fix.