The airline received considerable attention in 2007-2008 when it was hedged more so than most airlines when oil prices spiked -- a strategy that paid off handsomely.

Over the last decade or so Southwest's trading strategy has saved over $3 billion in fuel costs, said Chris Monroe, the airline's head of risk management.

Currently Southwest, which spent $6 billion on fuel last year, has hedges out to 2015. But the airline is basically unhedged through the first half of this year, meaning it thinks fuel prices will continue falling for at least another month.