Gotta admire honesty. From Zinsser Cover Stain Water-Base:
Cover-Stain Water-Base blocks stains from water, nicotine, smoke damage – even tannin bleed from cedar – as well as oil-soluble stains like grease, crayon, tar or asphalt,
usually in just one coat.
I recently did a never before painted popcorn ceiling with CS WB and I applied 2 coats of primer to it. I would have mopped it on if I had a way of doing it. The first coat absorbed into the ceiling, the second coat left it nice and white.
Here is the first coat. Photo taken quickly after I rolled it heavy and in a one-pass motion being careful not to roll an area twice.