Odds are you haven’t flown a small single-aisle aircraft like a 737 or an Airbus A320 across the Atlantic. But you could get your chance in the next couple of years – and one airline is promising one-way fares as low as $69 on the new planes.

The few 737s and A320s currently going over the pond either have a sharply reduced number of seats so they can exceed their normal range, or they’re between two points as close as you can get over the Atlantic, like WestJet’s flights between far eastern Canada and Scotland/Ireland. But the new generation of these aircraft will make longer flights possible with a full load.

Boeing’s 737 MAX and Airbus’ A320neo can fly about 500 miles farther than earlier versions, and use 15 percent less fuel. That will permit flights up to 3,000 miles between the eastern U.S. and western Europe. The initial operators of the planes will include Norwegian Air, JetBlue, and TAP of Portugal.

And a Norwegian Air executive this week told Business Insider UK that his airline plans to use the new aircraft to offer $69 transatlantic fares – about half the level of its current lowest fares. Norwegian has ordered 100 Boeing 737 MAX 8s, and it should start to take delivery sometime next year.

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“I can promise you that you will see trans-Atlantic flights on the 737 MAX next year,” Norwegian’s chief commercial officer Thomas Ramdahl told the publication in an interview, “and that’s when you will see the $69 fares.” The airline has also ordered 30 A320neo LRs for delivery starting in 2018 – a plane with slightly more capacity and longer range than the new 737s. He did not say which routes might offer the super-cheap fares.

Norwegian currently relies on Boeing 787 Dreamliners for its fast-growing transatlantic network, like its recently announced new service to Barcelona from Oakland, Los Angeles, Newark and Ft. Lauderdale.

JetBlue has ordered 30 A321neos, some of them likely to be the long-range version, prompting a lot of speculation about the carrier’s transatlantic intentions, although JetBlue has not said definitively that it will fly to Europe.

How would you feel about flying a 737 across the ocean? Please leave your comments below!

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