You might also try this stuff I've been using for years... Works awesome.
It's called "Magic Wadding" but has been known to have different names, depending on where you get it. You can find it in auto and boat stores, generally. It's an all-purpose metal polish.
It's basically a rough cotton wad, soaked in cleaning/polishing agents. It works on precious metals, aluminum, steel, copper, brass... You name it. It works fantastic.