I've been turning some brass the last couple of days, and had been getting very rough finishes using my new Glanze indexable tooling. A couple of weeks back, however, I'd bought a couple of inserts for aluminium cutting from Chronos:
Linky thing. Figuring that brass is softer than steel, it had to be worth trying it out. And, like wow (as a Californian might say):
After a simple turning operation, the machine marks are almost invisible to the naked eye. This pic is after a 0.005" cut @ 400cuts/inch (2.5 thou per revolution - the best my lathe will do):

So then I tried a facing cut... I didn't quite cut all the way through the marks, but you can see the quality of finish:

Suitably impressed, I broke out another product I recently bought, having seen it on here:

After applying a smear on the end & letting the lathe spin it for maybe 30-40 seconds (any more an I lose patience), this is the result:

It was proving quite difficult to photograph with the flash (the light just bounces off & goes somewhere other than in the camera), so I tried one without:

OK, it's not quite as good as a bathroom mirror, but not half bad for 5 mins of turning & half that polishing....