You should have more unlit in the basket, yes. It also sounds like the basket is kind of small for long cooks. Most responders you'll get will tell you that they fill their basket up, with wood chunks mixed in with the unlit coals, and then start with some lit briquettes to start it up. once you're done cooking close your intakes and exhausts, the fire will choke out and you can use whatever charcoal you didn't burn the next time you cook.
You might want to consider replacing the charcoal basket. Mine's 14" diam X 9" tall and I'm very happy with it.
Last edited by smokainmuskoka; 01-24-2013 at 09:05 PM..