Mike - The only way to truly know if your Breville burr grinder will grind fine enough for your Gaggia Classic is to try it and see. If it does not, then I suggest the Capresso Infinity burr grinder as your replacement. At $140 or less, I have found that it does an excellent job of grinding beans for the Gaggia Classic, which I own. I most always have the Capresso Infinity set to the second finest setting for perfect results with my Classic, and an extraction time of 22 - 30 seconds. My experience with this burr grinder proves to me that you do not have to spend more on a burr grinder to get perfect shots from your Gaggia Classic.