How to find the source of engine miss?

I have a stock, factory build, 1977 440 that is developing a miss (or runs rough). It doesn't run smooth. I don't know if it is ignition or perhaps due to a defective lifter. The carb is a new 750 DP, but it did the same with the previous carb. I need to do a compression check, but assuming that's ok... what?

Any thoughts on how to track down the actual source of the problem?

I am far from the most knowledgable person here, but I wouldn't suspect a lifter at all. Could be ignition or fuel. I would start with easiest things to check, such as timing, condition of distributor cap and rotor, and plugs and wires. Is the choke connected? Maybe sticking. The piece of paper over tailpipe to see if it gets pulled back in during idle can indicate exhaust valve problem, which could cause rough idle and a miss. Inspect all your vacuum lines to ensure there isn't a vacuum leak. These are free and easy checks to start with.

Thanks for the tips. No choke on this right now. After the easy checks, I'll replace the plugs and wires and see how it does.

How many miles on the engine and what type of ignition?

I don't know the miles, but it isn't new. No smoking though. Stock electronic.

Does it only miss at idle,under load,or all the time? You can richen the mixture to check for a lean miss by placing a rag over the carb inlet, closing the choke some,or misting some start fluid into the carb.You can check for a rich miss by removing a vacuum hose from the carb. If you think you only have 1 or 2 cylinders missing you can do a power balance test by removing 1 plug wire at a time from the distributor cap and noting rpm drop for each cylinder,then check out the weak cylinders plug/wire/cap terminals.If you have a miss/stutter under load check your ignition system(cap,rotor,wires,plugs,coil,etc).
Hope this all makes sense and helps.

The engine miss is at idle as well as under load. It's always there. I can certainly try the test involving removing each of the ignition wires.

The odd thing is that I cleaned all the plugs recently, and they didn't look bad before that, but it made no difference. I did not check each one for firing.

It doesn't sound like it is bad enough to be this, but.....did you happen to cross two plug wires at some point before it started it's rough running? I know I did it once and could have sworn there was no way I did it, so I didn't even check that until a week later. Couldn't believe I had actually done it, but boy was I happy it was just that.

Interesting idea, but yea, I don't think it's bad enough to be that.

To give an idea of how it feels, it almost feels like the stumble you get if you accelerate with the engine a bit flooded.