The trick is that CO2 pressure inhibits the yeast, preventing it from going into orbit all by itself. There is PLENTY of sugar in there!
Ferment until nicely carbonated (usually only a couple days) then refrigerate to slow the yeast way down and drink it up!
Happy Homebrewing! My buddies and I are moving up to 20 gal batches this year, I think -- we have a 24 gal boiler now.
Peter
