Surprisingly effective is "Axion Dishwashing Paste". It's a Mexican product made by Colgate-Palmolive. It resembles the goopy stuff in a tub you find next to many kitchen sinks in the Middle East. You can find it in your supermarket's ethnic aisle or cleaning products aisle.
I've found that the texture of this stuff effectively removes stains from cookware in a manner that is safer than even Bon Ami.
Rinses clean, no residue, gets rid of grease gently.
I've also found that Dawn can be problematic, as well as some of the smallified, superconcentrated liquids. A larger amount of a product like SunLight Sensitive, Original Ivory, regular concentration Ajax, or even Crystal White Octagon liquid is a lot better and cleans far more gently than the Dawn products, which just do "something" to the finishes of cookware that I don't understand and is hard to describe-but isn't good. I like the new clear "Palmolive with Bleach" as well, but I prefer the more dilute formulation.
I've found the Bon Ami product to be the best and least damaging to work with on better cookware-but I'd advise using it carefully and sparingly.
The liquid "soft" cleansers do more damage then they are worth, and furthermore leave unwelcome, stubborn residue.