There was a time when nearly every frequent flyer program let you tack a free stopover onto an award ticket. American, Delta and United have all long since scrapped that, but a handful of programs still allow it — and knowing which ones can turn a single redemption into two trips instead of one.

First, the vocabulary. A stopover is a stay of 24 hours or more in a connecting city between your origin and destination; anything shorter counts as a connection, and some programs cap connections at as little as four hours. An open-jaw means flying into one city and home from another — say, into Singapore and out of Bangkok. These distinctions matter because they determine how a program prices and permits your itinerary.

The standouts: Air France-KLM Flying Blue allows a free stopover even on one-way awards, including on partner airlines, though you currently have to phone the call centre to book it. Alaska's Atmos Rewards is nearly as generous — stopovers are free on inter-regional awards, bookable online via the multi-city tool, and because one-ways qualify, a round trip could include two stopovers. Imagine flying Japan Airlines from Los Angeles to Singapore with a free week in Tokyo built in.

Air Canada Aeroplan charges a modest 5,000 points for a stopover on a one-way award (not available within North America) and lets you book it all on aircanada.com. Emirates permits Dubai stopovers on one-way "Flex Plus" awards — which includes all first class redemptions. Singapore KrisFlyer allows one stopover on round-trip Saver awards and up to two on Advantage fares, capped at 30 days each.

The power-user options are more complicated but potentially spectacular. Japan Airlines Mileage Bank allows up to three stopovers on partner awards and a massive seven on oneworld awards (with an eight-segment limit) — though miles are hard to earn outside Bilt and Marriott. Asiana Club theoretically permits up to seven stopovers on Star Alliance round trips, but the rules are opaque, miles are tough to accrue, and the program disappears in December 2026 when it merges into Korean Air SkyPass. Turkish Miles&Smiles offers a free Istanbul stopover on round trips (phone booking required), while Etihad Guest allows Abu Dhabi stopovers on awards across a dozen partner airlines. British Airways Club works differently: pricing is per segment and distance-based, and there's a little-known multi-carrier oneworld chart that lets you string together up to eight segments with a stop in each city.

Why bother? Because a well-planned stopover can add a week in Tokyo, Istanbul, Dubai or Paris to your trip at zero or near-zero extra cost in miles. If you're flexible and patient with phone bookings, these programs effectively give you two holidays for the price of one redemption. Just note the rules shift often, and a couple of the most generous programs have expiry dates.