To save on flights, you'd better stop around

— -- With airfares breaking records, the fastest way to fly to your destination often isn't the cheapest.

Consider this: A family of four flying from Boston to Phoenix next week may save more than $1,200 round trip by taking a connecting flight rather than a non-stop.

Connections increase travel time and might add to the stress of a trip, but on routes between big cities, they can provide substantial savings, according to a study for USA TODAY by FareCompare.com.

"Non-stop flights garner a premium price in most city pairs," says Rick Seaney, CEO of FareCompare.com, which tracks airfares for consumers. "Flexible passengers with a choice of non-stop or a connection can save a bundle of money by booking a connecting flight."

Airlines have charged more for non-stop flights for many years, but the price differences have become easy for consumers to compare with the help of sophisticated search engines that can sort cheaper connecting fares at travel websites.

The technology is likely to be a boon for travelers in the months ahead. Seeking to cut costs and combat record jet fuel prices, airlines are eliminating or reducing the number of non-stop flights. That's putting more fliers on connecting flights.

"With huge domestic capacity cuts kicking in this month, we will see airlines pulling out of markets and leaving only one dominant non-stop player," says Seaney. "That means price-sensitive travelers will be well-served by considering connecting flights."

One-stop fares were cheaper on two-thirds of the routes. Connecting flights saved $50 or more on 28% of the routes and $100 or more on 16%.