I'm really picky about the whites that I buy, specifically for the reason you noted - many are so sheer. One of the best off-whites that I've found that I like was at Wal-Mart is 54" drapery lining. It's got a nice feel to it and is not a blinding white like many of the whites are. So it has a more vintage look to it. Also, the Kona whites are nice, I have some of those and really like them.