If travelers are booking a return trip there is a 15 percent discount.
These travelers may book these seats whether the ticket was purchased with cash or with frequent-flier miles.
A survey by the American Society of Travel Agents last summer disclosed that more travelers were booking adventurous trips than in the past.
In 2004, American Express introduced Web-based "variance reports" that point out any differences between what travelers booked and what they actually charged.
Currently, travelers can book a $269 "Midweek Madness" package through April 21 for a four-night stay and three-day lift ticket.
Other noticeable changes are that travelers are booking trips within driving distance from their homes and that more families are taking vacations together.
But some travelers are still worried about terrorism and are booking vacations within the United States or close to it, she said.
In Sofia the traveler can book the rest of the journey.
And travelers can still book the lower fares until the change goes into effect.
In recent months, more and more travelers have been booking trips on line.