Every fall in the United States, airfare prices take a dive -- after all, summer’s over, demand dries up and deals start busting out all over. This is especially true for transatlantic flights. If Europe is on your bucket list, or you know and love it well and are planning a return, now is the time to shop.

When to fly to Europe

Last week, I searched for flights to Europe for trips in late August through Dec. 15. Most were super-cheap fares for September or October (but remember, fares can and do change with little notice). Tip: Figure out the weeks or months you want to fly, then use a deal-finding tool to pinpoint the cheapest flights.

Cheapest cities of Europe

The best bargains can vary, depending on your home airport; bigger U.S. cities typically attract cheaper fares. Some general guidance.

• Best deals: London, Paris, Dublin, Madrid and Barcelona.

• Good deals: Copenhagen, Oslo, Amsterdam, Rome, Geneva and Zurich.

Are these the only bargains? No. We’ve seen very good deals to Vienna and Valencia. As noted, the deals are out there, waiting to be discovered. More examples found last week; all fares are round-trip for travel in the fall.

Fares from big U.S. cities

• Chicago – Barcelona, $393

• Chicago – Copenhagen, $464

• Dallas – Geneva, $566

• Dallas – London, $570

• Los Angeles – London, $371

• Los Angeles – Paris, $431

• Miami – Amsterdam, $360

• Miami – Dublin, $373

• New York – Madrid, $270

• New York Rome, $370

Fares from not-as-big U.S. cities

• Cincinnati to Paris, $400

• Detroit to Rome, $464

• Seattle to Vienna, $290

How to turn a good deal into a great deal

This is easy. Don’t insist on a nonstop flight. Sure, sometimes a direct flight to Europe is a bargain, but most of the deals I found included a stop. Connecting flights are not as convenient but you may be able to ignore any minor hardship if the savings are big enough and here are a couple of examples.

Chicago to Barcelona

• One stop: $391

• Non-stop: $1,359

Cincinnati to Paris

• One-stop: $400

• Non-stop: $995

Savings like this can help you put a nice dent in your hotel bill. Happy travels.

Rick Seaney is the CEO for FareCompare. Opinions expressed in this column do not necessarily reflect the views of ABC News.