NEW YORK >> Haven’t booked your holiday flight yet? Smart move.

The cheapest fares for Thanksgiving and Christmas aren’t going to the travelers who booked months in advance. Experts say they’ll go to those who can take advantage of some last-minute deals.

In previous years, the rule was nearly always the same: Travelers who booked earliest got the cheapest fares. Those who waited generally faced higher prices.

This year, though, things are different.

Yes, fares are up and flights are fuller, but those who’ve waited until the last minute to book Thanksgiving or Christmas travel can still find a deal if they know where — and how — to look.

In a year when airlines seem to have the upper hand, you may wonder why airfares on U.S. routes aren’t creeping higher as the holidays inch closer. The reason is airlines may have jacked some prices up too high, too fast. When that happens, airlines run sales closer to flight dates to fill the remaining seats on the plane. Airlines also ran many last-minute sales during the recession when Americans dramatically pulled back on flying.

For Christmas travel this year, you should get the cheapest flights if you book during the first week of December, airfare search site Kayak predicts. The average ticket price for travel around that time is about $433, which represents savings of about 6 percent, on average. In July, when many planner-types started locking down their winter plans, prices were as much as 27 percent higher than normal.

After prices peaked this summer, they began to gradually decrease in September. However, fares are expected to jump again starting in the second week of December.

You can also still lock in a fair price for Thanksgiving. Priceline says that the average Thanksgiving airfare has risen just $7 to an average of $407 in the past four weeks. That’s about 6 percent higher than last year.

For late December travel, the deals are even better. The average winter holiday flight price has dropped by 5 percent over the last month, Priceline says.

Of course, most travelers don’t want to risk waiting for a good deal over the holidays and risk not being able to afford a trip altogether. Airlines say that demand is solid, which means that a plan to put off a ticket purchase could always backfire. But it can be worth taking a chance.

This rule is only holding true on domestic flights. Kayak says the lowest international Christmas fares appeared in July and were about 16 percent lower than normal.

And when you do book, here’s another rule of thumb to keep in mind: Don’t assume that making a connection will lower the cost. According to Expedia, average ticket prices for direct flights around Thanksgiving are 20 percent lower than those requiring a connection. That doesn’t mean that every direct flight will be cheaper than a similar flight with a stopover on the same route though, so search carefully.

Also, comparison shop at multiple airports if you live in or near a major city. For the Washington D.C. area, flights into Reagan National are up to 22 percent cheaper than Baltimore-Washington International or Dulles, according to Expedia. In New York, LaGuardia is up to 15 percent cheaper than Newark or JFK.

The traditional rules of airfare also apply. Tuesdays are generally the cheapest days to book; Wednesday is usually the cheapest day to fly, followed by Tuesday and Saturday. But for Thanksgiving, watch out for Wednesday: it’s when everyone wants to fly and it’s generally the most expensive.

Early morning flights are generally the cheapest and provide an extra bonus during the holidays: they tend to be on-time more frequently.

Still concerned you’re not getting the best deal? Check out some fare-tracking charts on sites like Kayak.com that allow potential fliers to monitor the best time to buy. Another method? A browser toolbar called "Invisible Hand" will scan other websites while you’re booking and let you know if it finds a better deal — and where to find it.