My Dad's old Craftsman runs good, but every so often it will blow a puff of blue smoke and choke down a little bit, then straighten out again. Any ideas?

Maybe over filled with oil a little bit?

That did cross my mind. I'll keep after it.

Someone put a couple beans in the tank ?
You'd likely get a "puff" periodically.

That’s my guess too. Half way up the cross hatches is best for a lot of small engines that may not always be ran on the level.

what's that mean: "level"??

Ha! That’s what the engines on my mud motors ask! Always up and down.

Try fuel treatment, Sea Foam for just one. I promise you more will follow…lol

Oh wait you wrote blue smoke. Might be wrong answer!

gas is leaking into the crank case when idle =raising the oil level = burn off = white smoke
water in the carb and a drop gets through = white smoke

The Honda motor on my snow blower and several generators I have leak fuel into crankcase if the shut off valve is not closed. Smokey exhaust!

if I tip my mower up to clear a jam then start it up again I can expect blue smoke for a few seconds

so over full , mowing steep slopes , when you put it up in the truck , ect could cause it

and soon to be rings going a scratching.

You can smell the dip stick to see if the oils gassed up. If so, change oil asap. Don’t fill oil past 1/2way up the hash marks or half way between add & full.

Some Honda and Predator motors are bad for tank pressuring and overflowing carb if gas isn’t shut off and they are parked on the sun.

Good advice! Lots to do.

Valve seats on older mowers come loose and will float around some causing oil to get into cylinder and burn.

Is it a twin cylinder briggs with a double barrel carb? They were known for that if it is. The carb is an over complicated piece of junk. The o rings dry out and leak fuel into the carb causing blue smoke and what sounds like it's being choked. I have worked on a lot of craftsmans with that issue. We usually replaced the carb to fix the problem.