When I was in the USA recently, I wanted to change my flight home. I looked at AA.com for return flights from the USA to Belize to get an idea of what was available. Flights booked within a week in advance were all under $350usd return. So, there must be something to booking very late. I know this wouldn't work for many people, but I was stunned by the low fare. I should also thank AA, who only charged me $21 for changing my ticket home.