One of the biggest mistakes that Americans make while planning a trip to Europe, in summer or any season, is myopically focusing on a specific route. You want to visit Amsterdam, so you only search into that airport. Or you want to visit Glasgow, so you neglect to look at a map and consider, maybe, Inverness.

Or you only look at a particular airline and ignore some of the under-the-radar discounters such as XL Airways, Condor, Wow, Norwegian, and Thomson.

But flights to Amsterdam are $1500 round-trip this summer? Singapore Airlines recently had New York to Frankfurt for $799 round-trip nonstop. And Frankfurt to Amsterdam is just $106 round-trip on KLM this summer. Or take the train. It's just four hours.

Indeed, Frankfurt is one of the cheapest European gateways. recently sold Providence (yes, Providence, R.I.!) to Frankfurt for late August travel for $734 round-trip, nonstop.

Flights to Glasgow $1200 round-trip? Aer Lingus recently had July fares to Inverness for $777 round-trip, summer travel.

Rome too pricey? How about Milan instead? It's one of the cheapest airports to fly into this year, and Emirates recently had a two-for-one sale from New York, even in business class for $1898 round-trip, summer travel.

Paris on United too high at $1200 in early September? XL Airways recently had New York to Paris for $543 round-trip for most of September (and spring travel as well).

And keep in mind that fares fluctuate all the time. Literally hour by hour and there's no best time to find a low fare. This San Francisco to Stockholm $694 round-trip fare on American popped up on a Sunday. By Tuesday, it was gone. Ditto this LA to Denmark $641 round-trip July fare on Lufthansa and a San Francisco to Stockholm for $627 round-trip, peak July travel, on SWISS and Lufthansa. So sign up for airfare alerts by email.

Caveat: Don't make tight connections

If you do decide to fly from or into a cheaper destination and travel onward from there, do not set yourself up for failure by arriving at 10 a.m. and scheduling an onward journey to your intended destination that day. If your flight is canceled or delayed, you'll be out of luck. Instead, consider the "positioning city" as a bonus stopover. Explore the Black Forest for a day during your Frankfurt layover. You'll still save money and get two destinations for the price of one. If it's cheaper to fly from Providence to Frankfurt than from, say, New Orleans, sure, take a cheap Southwest Airlines flight to Providence but don't expect to leave onward on Condor that same day to Frankfurt. I've heard too many heartbreaking stories of people missing their connections.

One more tip: One-way fares

Most mainstream airlines charge almost as much (or sometimes more) for one-way economy class fares as they do for round-trips (which is why some travelers only going one-way actually buy a round-trip fare and don't use the return). Not so for the discounter airlines to Europe mentioned above (XL Airways, Condor, Norwegian, etc.). So you may save money by combining airlines rather than giving all your business to a single carrier, buying a one-way outbound on, say XL to Paris, then take a train or internal flight to, say, Copenhagen and fly back to the U.S. on Norwegian.

Bottom line: Armed with an atlas and your favorite airfare search engines, you can save hundreds by focusing first on crossing the Atlantic and using other flights, train trips, or other modes of transportation to get to your final destination. And look at connecting cities as a great way to break up a long trip and see two destinations for less than the price of one.

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