One of the few sectors left behind in the sharp April rebound has finally taken off. European airlines have rallied hard in the past few days, spurred by bailouts and economies reopening. Full recovery may still be a long way down the line, but investors don’t want to be left behind.

The Bloomberg EMEA Airlines Index has finally broken out of a tight range that held for more than two months. The index is up 32% since May 15, but such was the extent of the sector’s drop that it’s still down 45% for the year.

There’s been a string of positive news recently for the sector. Economies are slowly reopening across Europe, and tourists on the continent are likely to be able to travel this summer, even though Germany’s decision on travel warning was postponed to June 3. At a corporate level, there has been government support or bailouts for legacy airlines such as Air France-KLM and Deutsche Lufthansa AG.

Bailouts and state-guaranteed loans come at a price though. Airlines are likely to end up with high levels of debt and potentially less management flexibility in cases where states become shareholders. In Lufthansa’s case, note that the EU already made some demands on airport slots, while Ryanair Holdings Plc said it will appeal the aid. As for Air France-KLM, the carrier already started talks with unions to cut staff and capacity.

According to airlines association IATA, 55% of government aid made available to airlines due to Covid-19 crisis will create debt. Overall, airlines’ debt is expected to surge from $430 billion at end-2019 to $550 billion at end-2020, a nearly 28% increase.

This wouldn’t be a major problem if demand was expected to pick up fast, but that’s hardly the case. For example, British Airways already warned it doesn’t see demand reaching pre-crisis levels before 2023.

Other changes prompted by the pandemic will also weigh on the sector. The U.K.’s decision to impose a fortnight’s quarantine on travelers entering or coming back to the country is a blow to the industry, given Britain is by far the biggest European market by ticket revenue, according to IATA, and also the least “state-sponsored,” as shown in the chart below.

Profitability will likely continue to suffer, especially given that company travel isn’t expected to recover rapidly either. Just a 1% impact on corporate volumes would erode airline profits by 10%, Citigroup Inc. analysts say. They also generate 40% of revenue, with only 15% of passengers. Looking at the chart below, the rout in earnings forecast is unprecedented, and some recovery on that front may be needed to justify further gains.

Looking at single stocks, Ryanair and Wizz Air Holdings Plc are the only two “investable airlines,” Citi analysts including Mark Manduca said on Monday. According to them, both IAG SA and EasyJet Plc are likely to raise more capital in the coming months, while there is very little equity left in Lufthansa, no matter how much money the German government provides the airline.