Autosol with a dremel polishing set, then final clean with copper or silver polish, I find Goddard's long term polish to be the best, as it is I believe supposed to leave behind a tarnish inhibitor to maintain a longer lasting shine, and it does.
Did the ally an the bike recently, and the finish is mirror shiny, a deep pleasing shine
Despite the fact I like the raw aluminium bits on my bike to be shiny, there is a practical reason for this too, mud and musddy water doesn't tend to stick as well to shiny things, less cleaning !