• If you're willing to go on Christmas Day, New Year's Eve, or New Year's Day, you'll probably find space, but nothing at great bargains.

• Getting flights back on the weekend of January 5-6 is tough—it's the busiest weekend in the season. If you can come back after January 6, that opens a lot more possibilities.

• Broaden your horizons. Destinations like Argentina are sold out completely, but Chile is not as popular, so you have a better chance of getting a flight to Santiago than to Buenos Aires.

• Look for travel companies that offer daily departures on their packages (versus ones that only have weekly flights). This gives you more flexibility to find a good airfare.

• Don't be daunted just because the place you want to visit requires a visa (Brazil, for example). Tour operators have longstanding relationships with visa-processing companies that allow them to expedite a last-minute visa request (although it might involve a "rush" surcharge).