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Explore Reykjavic, Iceland, when you add a stopover while flying on Icelandair. Andreas Tille

Want to visit two amazing international destinations for the price of one? A little-known travel hack lets you add a stay in another city to an international trip for little or no extra cost in airfare.

Many major international airlines offer stopovers -- stays of 24 hours or more during which travelers can leave the airport -- in hub cities before you continue on to your final destination. And these cities are often exciting destinations on their own. Visiting Copenhagen? Add a stay in Reykjavik, Iceland, for a couple of days. Traveling to London? It may sound counterintuitive, but you can also book a reasonably priced fare on Turkish Airlines and take a few days to explore Istanbul.

“These routes are often cheaper, less crowded, and sometimes they even mean you get a bonus vacation,” travel expert Peter Greenberg said.

A few airlines, like Icelandair, explicitly advertise their stopover programs, but others just allow the option to book these itineraries through the “multi-city” options on their websites, usually for the same or slightly higher price.

For example, a search on Kayak.com shows that you can get a round-trip ticket from New York to Bangkok in December on Japan Airlines for $1,118. The itinerary includes a four-hour layover in Tokyo. But if you want four extra days instead of hours in Tokyo, searching for a multi-city itinerary turns up a ticket for $1,188, a difference of just $70.

Below are a few international carriers that offer free or very cheap stopovers in major cities:

Icelandair

Iceland’s flag carrier, which serves routes from 12 North American cities to 24 cities in Europe, offers free stopovers for up to seven nights in its hub city of Reykjavik. Its Iceland Stopover website makes it easy to book.

Emirates

The Dubai-based airline advertises a Dubai stopover package that includes a complimentary 48-hour visa. (Citizens of the U.S. and much of Europe don't need visas in the United Arab Emirates for up to 30 days.) The packages, which include your hotel stay, cost “as little as $48 per night” and must be booked through Emirates after you purchase your round-trip ticket.

Turkish Airlines

This airline doesn’t advertise its stopover policy, but it’s pretty easy to search for multi-city trips with Istanbul as the city in between. Most fares that include a few days stay in Istanbul cost about the same as one that only includes a brief layover.

Japan Airlines

If you fly Japan Airlines, you are entitled to a free stopover in either Tokyo or Osaka. The carrier’s web site has a “make stopover” tool that can help you book, but according to travel planning site Hopper, it turns up prices that are slightly higher than the ones you’ll find if you just search for a route as a round trip. But because the airline’s fare conditions state that up to two free stopovers are permitted on almost all ticket types, you can contact the airline directly to book the stopover fare at the lower rate.

Singapore Airlines

This highly ranked airline offers free stopovers in Singapore, and they’re fairly easy to book through the carrier’s website. Singapore Airlines also offers stopover packages that starts at $43 SGD (or $34 U.S.) and include hotel accommodations and airport transfers.

Finnair

You get one free stopover per flight in Helsinki, while a second stopover costs $100. Search the Finnair website for multiple destination itineraries. And your savings could be big: According to SmarterTravel.com, a search for a round-trip ticket from JFK to Amsterdam with a layover in London cost $1,300, but a multi-city route with a stopover in Helsinki was just $900.