When is the best time to book that flight? It’s one of the most fraught decisions travelers face, as ticket prices often fluctuate right up to departure time.

Recent fare analysis by the Airlines Reporting Corp. seems to challenge the conventional wisdom that the earlier you book, the less expensive your fare will be. In January, the corporation, which processes ticket transactions for airlines and travel agencies, reported that over the past four years passengers paid the lowest price for domestic flights when buying just about six weeks in advance.

To determine if that six-week sweet spot would hold true for international routes, I asked the company to analyze fares for several trips, like a summer vacation to Europe and a winter escape in the Caribbean.

Not only did the six-week period fail to stand up, but the findings indicate that the window for booking the cheapest ticket for these trips has increased over the past three years; in some cases it’s up to 24 weeks.

“Consumers have been getting the best prices a bit further out year over year,” said Chuck Thackston, managing director of data and analytics at the Airlines Reporting Corp.

Sure, it’s possible that if travelers pull back on spending, airlines will be forced to cut prices, allowing travelers to nab a cheap summer flight to, say, Barcelona, as little as three weeks out.

“If they don’t see bookings materialize the way they’d like, they will put the route on sale,” said Henry Harteveldt, a travel industry analyst.

But Harteveldt and other travel watchers agree that booking well in advance is a safe bet. So far this year, airlines have raised rates three times, said Rick Seaney, chief executive of Farecompare.com, which tracks ticket prices.

“I think pricing is going to be crazy,” particularly this summer, he said.

So if you place stock in historical trends, the message is clear: Act now.

For guidance, here are the booking windows during which passengers paid the lowest price for flights to popular vacation destinations last year, based on data from the Airlines Reporting Corp.

Europe in summer

Last year’s sweet spot: 21 to 22 weeks in advance

You may already be too late to score a cheap flight to Europe this summer. The booking window for the cheapest tickets has moved further out, from 11 or 12 weeks in advance in 2009 to 21 or 22 weeks in 2011. (Average round-trip fares rose to about $1,500 last year from $1,100 in 2009; this year’s outlook is no better.)

To boost your savings, take the least expensive route to Europe you can find. Then concentrate on getting to your ultimate stop cheaply.

“I look into the cheapest fare into a hub like Berlin,” said George Hobica, founder of Airfarewatchdog.com, which scours the Web for bargains. “Then I figure it out from there.”

He said this may involve taking the train or flying a budget carrier like easyJet or Ryanair to the final destination. Spanish airports like Madrid tend to be cheaper than London or Paris, he said. Dublin and Shannon also tend to be cheaper jumping-off points.

Caribbean in winter

Last year’s sweet spot: 11 or 12 weeksIn 2009 and 2010, the cheapest airfares went to procrastinators who purchased tickets just two weeks in advance at a saving of about 8 percent. But last year, the pattern took a sudden shift, with the cheapest tickets bought much further ahead.

“Certainly you’ll want to start shopping plenty early to get a gauge on pricing,” said Seaney of FareCompare, who recommended hunting for airfare as early as three months in advance, especially for hot spots like Costa Rica and out-of-the-way islands, which lack the airline competition that tends to keep prices in check.

Business or first-class to Asia

Last year’s sweet spot: 23 to 24 weeks

While the majority of premium travel is purchased by business travelers booking within six weeks of departure, leisure travelers with the flexibility to buy well in advance have been able to find bargains. Travelers paid about $3,113, or about 20 percent less than average, when buying premium tickets to Asia 23 or 24 weeks ahead last year.

A good time to take advantage of low business-class rates is during peak vacation times like summer or the winter holidays. While coach class quickly fills up with leisure travelers, the cushy seats at the front of the plane can be empty. Rather than give those seats away as upgrades, airlines often try to fill them with sales, according to Joe Brancatelli, publisher of the travel website JoeSentMe.com, which alerts members to such sales.

General tips

Beyond historical trends, there are also some useful online tools that can help you evaluate fares. For example, Bing.com offers a Price Predictor that uses algorithms to determine how likely a fare is to rise or fall during the next seven days. It applies to flights from more than 250 cities in the United States and to top domestic destinations and major hubs in Europe.

If you decide to wait in the hopes of a price drop, sign up for fare alerts offered by practically every travel site, from American Airlines to Travelzoo. Yapta.com, another price-tracking service, alerts travelers when the price of their plane tickets drop after purchase, allowing travelers to request an airline voucher for the price difference.

For the cheapest dates to fly, go to Itasoftware.com, which allows you to scan an entire month’s worth of fares. To buy, you must go to the airline’s website or online agencies like Travelocity.

Finally, buying two one-way fares on separate airlines can be cheaper than the best round-trip price. Kayak.com calls such tickets “hacker fares.” A recent search on the site for a flight from Boston to San Juan, Puerto Rico, turned up a fare of $313 on Delta to San Juan, returning on US Airways, compared with $349 round trip on US Airways alone.