NEW YORK (Reuters) - The lowest fuel prices for more than a decade are proving to be a double-edged sword for U.S. airlines.

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While carriers saved hundreds of millions of dollars from oil prices halving since June, they forfeited a large chunk of that gain because of the fuel hedges they bought as protection against oil rising.

The bulk of those hedges - which effectively lock in fuel costs in advance - are set at levels that force airlines to pay more for fuel than current market prices, turning them into a hindrance rather than a help.

As a result, three of the four biggest carriers - Delta, Southwest and United - said this week they were rethinking their hedging tactics. Meanwhile American, which does not hedge fuel costs at all, is reaping the biggest savings.

Southwest Airlines Co said on Thursday its outstanding hedges represented a loss of $1.8 billion through 2018, at Jan. 15 prices. However, it still expects a fuel bill that is more than 30 cents per gallon lower this year compared to 2015, or a roughly half-billion dollar net benefit.

The budget airline has exited some contracts so that 30 percent to 35 percent of its fuel consumption in the second half of 2016 is covered by fuel hedges, down from 60 percent to 70 percent, its Chief Financial Officer Tammy Romo said on an investor call. She did not say how much it paid to rid itself of the hedges.

“While our hedging philosophy has not changed, our tactics have in this environment,” said Romo. “We will focus on catastrophic protection with no downside risk,” she added, referring to more expensive hedges that cap the price an airline will end up paying for fuel.

Delta Air Lines Inc said on Tuesday it has exited hedge contracts for 2016 at a cost of $100 million to $200 million per quarter in order to pocket each dollar that fuel prices decline. It forecast savings at $3 billion this year.

“You could have made this call a while ago. The pain wouldn’t have been so bad,” aviation industry consultant Robert Mann said, noting oil oversupply is expected to continue as sanctions on Iran lift and the country pumps extra crude into the market.

United Continental Holdings Inc has not added new hedges since July and is evaluating its hedging program structure, acting Chief Financial Officer Gerry Laderman said on the airline’s investor call on Thursday.

At the same time, United said the oil rout has hurt sales to energy clients near the airline’s Houston hub.

To make matters worse, lower fuel costs have given big carriers room to chop fares so that smaller, low-cost rivals do not undercut them, leading to revenue-draining price wars.

The big winner is American Airlines Group Inc. The world’s largest carrier said its fuel cost was between $1.48 and $1.53 per gallon in the fourth quarter because it has not hedged fuel at all - better than Delta, United and Southwest by some 30 cents or more.