Here is a goal: How can I get rid of old stains in a ceiling?

Which way makes more sense to accomplish this goal?
Try spraying a mix of 10% bleach to water on them and wait 24 hours and more often than not, those unsightly brown spots will have disappeared, this will clear up most stains on flat or popcorn ceilings, just be sure to protect your eyes and anything close by that could get bleach on it.