I am a jeweler and have a giant polishing machine/vacuum setup that's great for handling precious metals which rely on heat to literally 'move' the metal. That means that together with the compounds, the speed of the wheel and the technique make jewelry shine.
With pipes I found out that different techniques must apply. My machine runs at 3450 rpm and i typically use 5 to 6 inch wheels-extremely high speed and lots of heat.
My first attempts were to handle it like jewelery--a no no. I burnt the stems and did nothing good to the bowls.
I had to alter my techniques to first, apply the polish to the wheel (sparingly while its running) and just lightly move the pipe to the wheel. Much better results. Not to make this a whole lesson, the polish and pipe are applied at the lower third of the wheel while its rotating, NOT THE UPPER TWO THIRDS. DANGER! The pipe can easily be ripped from your hands, and one should always wear eye protection!
For those without these machines, the above suggestions of low speed motors and 4 or 5 inch wheels with gentle pressure should give good results. Polishes can include: Tripoli for deeper but fine scratches (meaning no gouges, in which sandpaper of different grits would be used first); If there aren't any deep scratches, i would go straight to white diamond followed by carnauba wax, hopefully each on separate wheels, cleaning the pipe inbetween each step as to not transfer one media to the other one.