Painting - getting rid of old drips or runs in paint

On occasion I find runs in the paint that I have missed or I need to paint over somone eles's drip or runs. When the run is wet, no problem but when it has dried, I can't even seem to sand it down because the sandpaper fouls with the paint or it still leaves the run marks. Maybe I use the wrong sandpaper or am giving up too soon. I have actually mudded a couple of these to get rid of them but there must be a better idea. What do you pros do?

Not drip
:D

Really I scrape them off with a putty knife
If it's an old one, and I catch it before I put the new on, I might sand a bit, but only to feather it after I shaved it off
If it's one I made (it happens ;)), I use the putty knife, then touch up If I have to, I never sand those, it just goobers them up worse
If it's super fresh I might try and wipe it up, or wipe it off completely and repaint

I agree with slickshift. Sanding out runs is usually a waste of time. Scraping the run off with a putty knife or even cutting it out with a razor blade and then patching with spackle or joint compound is easier and more effective.

Regular sandpaper doesn't work well. Use a drywall sanding screen to smooth it after using the putty knife.

Thanks for your advice. Appears the most effective way is the don't-drip method so I will work on perfecting that one. :D

When I was a painter apprentice an old journeyman told me there is no shame in making a mistake in your work - THE ONLY SHAME IS IN LEAVING IT :)