Airline executives are feeling the headwinds of the growing alarm among travelers about the climate consequences of air travel — and acknowledging their industry isn’t doing enough to curb emissions.

Air France CEO Anne Rigail told the audience of the Fortune Global Forum on Monday that flying shame had taken root in her own household among her husband and children. “It’s very good because I was not at all surprised by this whole thing about ‘flight shaming’,” she said. “I think it’s our biggest challenge.”

Flights account for about 2.5 percent of global greenhouse gas emissions, and some travelers, most notably Greta Thunberg, a 16-year-old Swedish climate activist who gave up flying, are cutting back on flying to reduce their personal carbon footprint. The Swedes have even coined a word for flying shame: flygskam. An October survey of 6,000 travelers in the US, France, Germany, and the United Kingdom found that one in five travelers had reduced the number of flights they took in the past year.

Rigail’s remarks were followed on Wednesday by praise from Tim Clark, the president of Emirates, of the attention environmental activists like Thunberg have drawn to the problem of airline emissions.

“[W]e [in the aviation industry] aren’t doing ourselves any favours by chucking billions of tons of carbon into the air. It’s got to be dealt with,” Clark told the BBC. “I quite like Extinction Rebellion and Greta Thunberg for having brought a real focus to the issue; a focus on the fact that we are not doing enough at the speed we should be.”

These business leaders haven’t said what they’ll do about climate change, and this week Emirates announced a $16 billion order for new aircraft. But their comments show that flying shame isn’t just a fringe movement that the industry can ignore.

Shortly before its collapse in September, airline Thomas Cook said that the environmental movement against air travel was hurting its business. Scandinavian airline SAS and Sweden’s airport authority have also reported declines in air travelers that they blame on flight shame.

Over the summer, Dutch air carrier KLM launched an environmental campaign that obliquely acknowledged the flying shame movement, encouraging customers to “fly responsibly” and to be judicious about their air travel. KLM CEO Pieter Elbers also wrote in a letter that “we invite all air travellers to make responsible decisions about flying.”

However, environmental activists aren’t united behind the message of flight shaming. Some argue that the focus on personal habits like plane travel shifts the burden away from the larger institutional changes needed among businesses and governments to combat climate change.

And while some air carriers are reporting a slowdown in ticket sales, others don’t seem to be affected at all. Finnair, for example, reported an increase in passengers this year. The overall market for air travel is poised to grow dramatically, particularly in regions like China, Southeast Asia, and sub-Saharan Africa.

Air travel is notoriously difficult to decarbonize. There are almost no alternatives to fossil-derived jet fuel that can deliver the energy density needed to cross oceans by air, at least at a price that passengers can afford. If a carbon-neutral jet existed, “we would immediately buy one”, Rigail said Monday.

The growing awareness of air travel’s impact on the environment has helped inspire a renewed push for cleaner air travel technologies — electrification, biofuels, electrofuels, and hydrogen — but these tactics may be decades away from making a dent in air travel emissions. That means there are few good options for the climate-conscious traveler in the meantime other than simply flying less.

This tension between rising air travel demand and mounting climate change concerns is creating more uncertainty for the airline industry. To help address this, the United Nations is working on setting up an emissions trading scheme for airlines to offset their contributions to climate change.

Thunberg, for her part, is currently sailing back from North America to Europe to attend the United Nations climate conference in Madrid, Spain, in December. At the meeting, groups like the European Union plan to press the airline industry to do more to limit their emissions.