Lower oil prices gave most U.S. airline stocks a bounce last week — not a surprising development since fuel accounts for as much as 40% of an airline’s operating costs. JPMorgan (NYSE:JPM) analyst Jamie Baker last week estimated that the savings from lower fuel would create $5.5 billion in annual “windfall” profits for the airlines.

While lower fuel prices are good news, airlines have lots of other problems, so be choosy when playing the sector.

Here are four reasons to doubt the sector’s latest attempt to ascend:

Fuel Price Volatility

It’s not just high jet fuel prices that are eating airlines’ collective lunch — it’s wild swings in fuel prices. Carriers make very precise measures of supply and demand, and determine how to get the most bang for their fuel buck.

In the commercial aviation industry, that’s known as capacity planning. When fuel prices are high, airlines are more likely to reduce capacity by filling all the seats in smaller, more fuel-efficient aircraft. When fuel prices are low, they can increase capacity by flying larger aircraft.

Although most airlines try to mitigate high fuel prices with tactics like hedging (or in Delta Air Lines’ (NYSE:DAL) case, buying an oil refinery), they can also lose big when fuel prices fall unexpectedly.

The Mess in Europe

The situation in Greece will keep casting a pall over Europe in the near future — and the continent already had been headed toward recession. That’s bad news for U.S. airlines that fly there, like Delta, United Continental (NYSE:UAL), American Airlines (PINK:AAMRQ) and US Airways (NYSE:LCC).

U.S. airlines will need to decrease capacity to Europe as the year wears on. Airlines for America (A4A), the trade group that represents U.S. carriers, says airlines will cut capacity to Europe by nearly 8% in the fourth quarter of this year. That could be tough on earnings because Europe remains U.S. airlines’ largest international market. Delta already has announced plans to cut its trans-Atlantic capacity by 5% after Labor Day.

Higher TSA Taxes

Airlines aren’t getting a lot of help from Congress. A key Senate committee last week advanced a bill that would double transportation security taxes from the current $2.50 for a one-way flight segment to $5. That affects every airline including Southwest-AirTran (NYSE:LUV), JetBlue (NASDAQ:JBLU), Alaska Airlines (NYSE:ALK), Spirit (NASDAQ:SAVE) and SkyWest (NASDAQ:SKYW).

Although carriers will pass the tax hikes on to their passengers, revenue is still likely to take a hit. “It’s a simple equation: When you add taxes, demand for air travel is dampened, resulting in lost jobs and lost air service,” said A4A President and CEO Nicholas E. Calio. “Our customers today pay 20% – $60 on an average $300 domestic roundtrip ticket – of their ticket prices in taxes, on par with taxes for alcohol and tobacco, products taxed to discourage their use.”

Merger Hiccups

Consolidation has been proven time and again to be a good thing for airlines: It delivers broader reach, economies of scale and financial benefits. But marriage is easy compared to the daily challenges of living together after the honeymoon.

Delta’s combination with Northwest in the middle of the Great Recession was acclaimed as a success story, in large part because Richard Anderson, DAL’s chief, had spent more than three years running Northwest in the early 2000s. Even so, the merged carrier still struggled with its labor unions. United Continental is fightng through major computer integration glitches now, and its customer approval has plummeted.

Early into the process of integrating operations with AirTran, Southwest has made some progress — notably subleasing AirTran’s Boeing (NYSE:BA) 717s to Delta so that the combined carrier could standardize on the Boeing 737. AirTran, which already flies to Mexico, last week launched new international flights to that country and to Puerto Rico.

But Southwest’s flight attendants last week voted down a deal that would have allowed the carrier to fly internationally or over water. Thorny issues like these pose significant challenges for combined carriers it the near term.

Still, one airline has a good chance to buck these industry headwinds.

The One Airline Stock to Buy Now

That would be US Airways, which I like right now. One big reason: the growing likelihood that it will acquire American Airlines out of bankruptcy.

US Air CEO Doug Parker launched a charm offensive to get support from AMR’s unions for a merger deal. It appears to have worked because American’s three largest unions — the Transportation Workers Union, the Association of Professional Flight Attendants and the Airline Pilots Assn. — have expressed support for such a deal.

Daniel Akins, an industry analyst who testified on behalf of American’s flight attendants union, told a federal bankruptcy court earlier this month that AMR was “in a corner” and that a merger with US Airways was “inevitable.” In reference to AMR’s post-bankruptcy business plan, Akins said he had “never seen a business plan this bad in terms of the deficits that American faces.”

Not surprisingly, American rejected that view, remaining resolute in its intent to emerge successfully from Chapter 11 as a stand-alone carrier. “American Airlines is strong as a stand-alone company,” AMR attorney Jack Gallagher told the court last Friday. “American Airlines doesn’t need a merger.”

Still, if the two carriers do merge, the combination could yield $1.2 billion in annual savings. Yes, it would likely face the familiar integration challenges, but it won’t be in the thick of those difficulties until 2014, so there’s likely to be significant stock price appreciation in the near term.

LCC has a couple of other things going for it. Because LCC doesn’t hedge fuel like most airlines, it gains more from falling prices than most of its competitors that do. US Air President Scott Kirby said recently that his airline doesn’t hedge because of the “massive risk” created when prices fall, noting that three years’ worth of hedging options translates into paying $1 billion for an “insurance policy.”

US Air’s operational metrics — such as on-time arrival and departure, completion and baggage handling — posted all-time company records in April, and its 3% capacity growth is disciplined. LCC stock also set a new 52-week high last week. Currently trading around $12.40, the stock has risen by more than 200% since its 52-week low on Nov. 23 — five days before AMR filed for bankruptcy.

LCC has a price-to-earnings growth (PEG) ratio of 1.75 – one of the highest PEGs in the airline sector, indicating the stock could be overvalued. But its forward P/E of about 5 is a little lower than that of UAL and Delta (which are around 6) and much lower than LUV at 13 or JBLU at 9.

But is US Air already soaring too high? Despite its dramatic ascent, I think LCC still has room. Its fundamentals are pretty good if you like airlines (Warren Buffett, for example, doesn’t). If Parker can manage to seal a deal with American, the stock could be looking at an upside of 15% to 20% in the near term.

Obviously, the airline industry is a notoriously tough place to make money, so consider your tolerance for risk carefully before you ante up. And US Air has wooed two brides in recent years (Delta and United) that both got cold feet and eventually merged with other carriers. So, an American-US Airways merger is hardly a sure thing until a deal gets done.

Nevertheless, I think the odds are good that US Air win over American, and I rank LCC a buy with a price target of $15.

As of this writing, Susan J. Aluise did not hold a position in any of the stocks named here.