Imagine the prime minister showed up one night on national television for an emergency address to his people and closed his speech with the words “May God be with us.” Then it would be fair to assume that things looked serious. And the outcome would certainly be hard to predict.

But that is exactly what happened in Iceland five years ago. When Geir Haarde delivered his speech on Oct. 6, 2008, the country's three largest banks had just collapsed and with them, the economy. The national currency was only worth a third of the value it had 24 hr. earlier, and Iceland was in very real danger of going bankrupt, too. People were wondering whether there would be food in the supermarkets the next day. Travel demand evaporated within one afternoon. Nobody could afford to fly anymore.

Given the circumstances, it seems like a major surprise that Icelandair still even exists. But the carrier not only continued to fly, it also started one of the most unusual success stories of the global airline industry. It has doubled its capacity over the past four years and has ambitious plans to grow its fleet and network further. With the exception of 2008, the company has always been profitable in recent years.

Of course, one must not forget that in this period two of the island's 130 volcanoes (Eyjafjallajokull in 2010 and Grimsvotn in 2011) chose to erupt, seriously disrupting air travel for weeks. Icelandair was forced to relocate its hub from Keflavik to Belfast for weeks and managed to keep almost 80% of its normal schedule. Ironically, those eruptions have done much to promote Icelandair's growth even further. So it is not black humor that the airline has named two of its aircraft after the pair of volcanoes. (The entire fleet carries the names of different volcanoes.)

Icelandair and its predecessors have long been known as the “hippie airline,” offering a cheap transatlantic travel alternative for students like Bill Clinton, who used the carrier for his first trip to Europe in the 1960s and later became U.S. president.

While the hippie days are long gone, the airline is still essentially in a similar niche and has managed to define a sophisticated, unusual, hip business model in which it seems to thrive against all conventional wisdom. Its home market (300,000 people live in Iceland) is tiny. The carrier itself is not big and has to compete against three giant transatlantic joint ventures that control schedules and fares for more than 80% of the market. Icelandair is not a member of any of the three alliances and it operates a relatively old and fuel-inefficient fleet of Boeing 757s.

Nevertheless, the single most important reason why the model works is simple geography. Iceland is right underneath the great circle routes from Europe to North America. Flights into Europe are between 3 and 4 hr. long and flights to North America last between 5 hr. (Boston) and close to 8 hr. (Denver). In other words, Icelandair is the only airline that can use narrowbody aircraft for its entire route network. “Because of the geographic location of Iceland, we can fly single-aisles to the [U.S.] West Coast,” says Birkir Holm Gudnason, who has served as CEO since 2008. Its 757s fly to Seattle and reach the Deep South (Orlando, Fla.). The competition needs widebody aircraft to get to those destinations. It means a big investment, large markets and major risk.

Icelandair operates what it calls a “24-hour hub” at Keflavik International Airport. In the morning, its aircraft take off for all the destinations in the East. They reach Europe around midday and start the return flight early in the afternoon. Because of the 2-hr. time difference compared to most of Europe, the fleet is typically back in Keflavik at around 3-4 p.m. The North America operation starts toward late afternoon, which is not a problem because Iceland is already so far west from continental Europe. The fleet arrives in the U.S. and Canada in the early evening and returns to Keflavik the next day in the early morning, right in time to leave for Europe.

The airline is also a mixture of legacy and low cost. It has three classes: a business class, premium economy and regular economy. Business is not comparable to what others offer on transatlantic routes. It is more like a domestic first-class flight in the U.S., and in economy food is not free. “We believe in the hybrid concept,” Holm says. He does not want to disclose Icelandair's unit costs other than saying they are somewhere in between low-fare and full-service airlines.

Historically, the routes have been short enough for one aircraft to fly all of this and be back in time for the next turn. But Icelandair has slowly departed from the pure and most-efficient model by introducing more longer westbound routes. It could do so because of the low ownership costs involved with flying 757s. In 2009, it started parking aircraft in the U.S., sometimes for 20 hr.

Seattle was a turning point. Icelandair had been looking at introducing the destination before. It seemed ideal: It was right at the edge of the 757 range from Kevlavik, but it was already served by three European carriers – Lufthansa, British Airways and SAS Scandinavian Airlines. Then, SAS pulled out after more than 30 years of serving the market. As much as that decision was a symbol of the decline of what was once Scandinavia's dominant airline, it was also a symbol of the rise of Icelandair.

Seattle involved parking the aircraft because, had it returned immediately, it would have missed the morning departure wave to Europe in Keflavik. Icelandair decided to take the risk and keep it on the West Coast for most of the day. The first year was tough economically, one official says, but Seattle has since become one of the most profitable routes in the entire network.

Encouraged by the West Coast success, Icelandair was persuaded to deviate more from high utilization: Its aircraft also stay overnight in Denver, Orlando and soon in Anchorage, Alaska.

Transatlantic connections have grown to become by far Icelandair's most important business. Only a few years ago, they made up around 26% of its traffic. But the airline was forced by circumstances to reduce its dependence on its struggling home market. The share of connections had risen to 47% in the second quarter of 2013, and Holm says there is no real limit to where it can go “as long as it is profitable and the infrastructure in Iceland can handle it.” That also means the Icelandic home market is no longer a limiting factor to the airline's growth.

In 2012, its fleet consisted of 16 Boeing 757s, 15 -200s and one -300. Many of the aircraft are ex-Iberia and most have subsequently been equipped with winglets. The addition of winglets has been hugely important for Icelandair because they added around half an hour of possible flying time. Concerns about bad weather diversions are now a thing of the past for most sectors.

For 2013, Icelandair added another two ex-American 757s and next year the growth will be even greater. Three more aircraft will join the fleet as the carrier opens a trio of new destinations—Vancouver and Edmonton in Canada, and Geneva in Switzerland. While Vancouver was seen as a no-brainer since Seattle worked out so well, Edmonton is a different case: it has only one Air Canada long-haul flight, and while Edmonton is a big city, it is also unknown territory. But in many ways, it fits Icelandair's criteria: the airline is not after the most heavily traveled routes anyway, where the majors and their joint ventures dominate. It is trying to fly underneath their radar screen and connect markets where it has an advantage. The new Anchorage route, for example, cuts elapsed travel time to Europe by more than 3 hr.

The carrier is growing its seat capacity by 17.7% next year. Of that, 4.3% can be allocated to the new destinations, 7.2% to more European and 6.2% to more North America flying. Vancouver and Edmonton will have more than 80% connecting passengers, Icelandair predicts.

The last major turning point was in 2009—reducing dependence on the home market, becoming a bigger transatlantic player, remodeling aircraft rotations – and another one will be in 2018. That is when Icelandair will take delivery of its first Boeing 737 MAX. It has ordered 16 aircraft, a mix of 737-8s and -9s. The first three -8s will arrive in 2018, followed by four more and two -9s the next year. In 2020, four -9s and one -8 will be delivered and two more -9s will be accepted in 2021.

The introduction of the MAX will have a deeper influence on the business model than might be visible at first glance. Because of the higher capital costs, the MAX can't be parked anywhere like the 757. That may not happen much anyway because the aircraft will be used on shorter sectors, but the introduction of factory-new aircraft will also mean that Icelandair has to build an even less seasonal network.

The airline has historically parked a significant part of its fleet in the low-demand winter. It is already trying to even out the differences as much as possible. Betting on transatlantic connections does not make seasonality disappear, but the fluctuations are already not as large as they would be if the airline still depended more on the Icelandic home market. But even there, a lot is happening to attract tourism, even in the winter. A real tourism boom, not least caused by the volcano outbreaks that were responsible for severe but short-term operational disruptions, was another important factor contributing to Icelandair's already-steep growth.

The way the airline now deals with the fluctuations is by pushing all the heavy maintenance work into the winter while flying day and night in the summer. It also typically leases out two aircraft with the help of its sister company and charter specialist Loftleidir. This winter, the carrier plans to operate the equivalent of 14 aircraft, with some being rotated through heavy checks.

Because the MAX is smaller than the 757, the aircraft can be used on thinner routes. That will be one more important strategic advantage of the airline, because it will be even harder for its much bigger competitors to defend those markets. In thinking further ahead, the model could be expanded even more by using aircraft such as the soon-to-be-modernized Embraer 190/195s. Although range would likely be a limit for the aircraft to be used on North America flights, it would open up more opportunities in Europe.

The introduction of the MAX will not lead to the 757's retirement, which the airline plans to continue flying until around 2025.