random misfire problems?

The exhaust backfiring when you take your foot off the accelerator sounds like the diverter valve for the A.I.R. system. Hope that helps! Jim

A vehicle that is over 20 years old may have a leaky fuel injector if so equipped. If an injector has become leaky you will have the same symptoms.

This sounds very much like the problem I have with my 2008 GMC Sierra. I've been driving it like this for at least 10 years! I could not figure it out. What I thought was when the truck warmed up that was part of the problem, but i also noticed on a hot day, the truck immediately started to act up. Over the last year, I've been trying random things to see if I could affect this problem. This week, I woke up and had a particular interest in the fuel cap. Now I've bought and replaced the fuel cap at least twice to fix this problem but it didn't do anything. I noticed that the fuel cap doesn't seem to snug up, but kinda just sit there and rattle around (yes, even the new ones i bought). As I was refueling the truck, I literally just lifted the cap straight off without any twisting, and after refueling, it wouldn't snug up. This particular morning, I took the gas cap off an old generator I am tossing away and took the rubber washer off of it and put it on my trucks fuel cap and put it on the truck. It snugged up real tight! I've been driving it all week without any problems, even on a hot day. To think how much money I put into that truck to solve this problem. I took it to the dealer and they paid at least $2300, and it still had the same problem. The OBD-II codes only showed codes from when it was backfiring and had no power, so it was unhelpful. I suggest you check this out because I think the fuel cap has changed over the years, and the loose cap allowed air in the tank and wore out the fuel pressure sensor. Hope this helps.