been there, wetted and scraped off popcorn and refinished with skim coats, good way to even out dips in walls and ceilings to get really flat surfaces. Use lamp

You can cover it, but if you want to do a decent job, you’re going to have dust and lots of it. You can reduce it by lightly spraying the popcorn with a water mist before removing it, but it’s still going to be messy. Need lots of plastic drop cloths and a good industrial vacuum cleaner.

You haven't said if you mean "popcorn" or "knockdown" as a finish when you said "textured". If it's knockdown, I'd just mix up some mud, fill the voids, give it a light sanding, prime, and paint. You'll have to scrape the popcorn.

I agree with Joseph.The bad thing is if iy is popcorn and it was painted the best is just to cover it with 1/4” drywall.

What texture?

Popcorn - scrape off. If painted it can still come off - just plan on three scrapes.

Texture - float it with thinned joint compound. We use a 5 gallon bucket and paint roller on a pole - thick nap roller cover (1"). Thin the mud with water so it is like pudding. Plastic on everything to catch drops. Roll out several feet - flatten with a trowel. Work it while it is wet - not dry - to avoid sanding. Takes some practice - but this is faster and less mess than new sheetrock.

Sometimes depending on height restrictions it may be less messy, faster to just cover with 1/4" drywall

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But applying thin drywall that moves and flexes over a bumpy surface can lead to...a bumpy surface.

Thanks for all suggestions. Our ceiling wasn't popcorn and it was painted. Unfortunately, our painters just used traditional approach and covered it with 3 layers of compound and sanded it all at the end. It created a ton of dust.

Pro- tip, turn off the HVAC during the super dusty parts

It's going to make a lot of dust no matter what. Sanding will be required to make the drywall smooth after skimming after removing the texture or if you just cover it with new drywall. Smooth ceilings are especially finicky since they show every imperfection.

When you say "in one of our rooms" do you truly mean a closed off room with doors or narrow openings? If so, you can significantly limit the amount of contamination in the rest of the house. You could tack up drop cloths on both sides of every door to capture any dust that comes through cracks around the doors. If you have forced air heat, all vent openings in the room should be sealed shut with plastic and tape. Remove all furniture. If your room is really part of an open concept, you are probably out of luck.

I just went through this with my soon-to be-new home that's being remodeled. Every ceiling had popcorn on it. And I mean every. Every room. Every closet. Why, even the panel covering the access hole to the attic that's hidden in a closet. I'd take dark Mediterranean-style cabinets, avocado appliances and orange countertops any day compared to this rotten concept of a ceiling finish. It's all gone now (scraped, skimmed and sanded) and the ceilings look phenomenal. Fortunately, the house is empty so the dust didn't matter.

I should qualify - when I bought the place, the kitchen and dining area had smooth ceilings. As part of the remodel, those two ceilings had to be taken down for some extensive rewiring work. That's when we discovered that they also had popcorn. A previous owner had fastened another layer of drywall over it - securely screwed into the joists on nice 16" centers - and into the drain of the second floor master bath where the joists had been cutout to accommodate it.