A little background: I bought a 1966 M20E Super 21 last December. From the complete log books, I know that the engine was replaced in 1978 with a new IO- 360A1B6 and now has ~1050 hrs, with 2222 hours on the airframe. It was flown regularly until 2005 and then appears to have not even had an annual done until it was sold in 2013 to the guy I bought it from. He flew it an average of 10 to 15 hours/year. I know now (from about 30 hours of following this forum) that one of the worst things for these planes is to sit and not fly. My mechanic just completed the first annual which started as soon as I purchased the plane. I spent ~$5000 (which I expected as the last few annuals were basically rubber stamped). Mags rebuilt, new plugs, wires, hoses, etc. My CFI and I have flown a total of 6 hours over the last 2 weeks with no problems. Today we were in the pattern after a 2 hour flight at 2400 rpm when the engine suddenly started backfiring and running very rough. The runway was assured, and as soon as I touched the throttle, it immediately smoothed out. We landed and spent the next 20 minutes running up the engine on the ramp. At least 3 more times, when we hit 2400 rpm, it did the same thing. Both increasing and decreasing rpm immediately solved the issue. We let the engine cool completely and could not duplicate the anomaly again. Any ideas as to what could cause this?