Ask the experts about whether the ceiling cam be replaced. I do know they make special extra-fluffy rollers for painting textured ceilings.

I bought a foreclosure that needed the entire ceilings repainted. They were an awful grey throughout the entire interior. I bought the most expensive ceiling paint I could find and the highest nap roller, and repainted ALL of my ceilings. It was very time consuming but well worth the effort! Through trial and error I learned a technique so that the popcorn would not pull off with the paint. People will say to redo the ceilings but I think a fresh coat of paint did it for me. I am on a budget and do not believe in overremodling so that I will have more $ into the place than it will ever be worth.

When repainting "popcorn ceilings", be sure to only go over the areas once with the wet roller. The texture seems to soak up paint quickly, then will come off the ceiling when you roll over it again. Practice in the closets first!!

An alternative that I've decided I like MUCH better is to take a wide putty knife and scrape the bulk of the texture off of the ceiling before painting. This will leave a texture similar to that of what is often used on walls. I then painted over this with a semigloss latex paint so I could wash the ceilings as well as the walls.