CLARE MORRIS hardly noticed when she tore the meniscus in her knee while dancing. The pain started only when she heard that repairing the damage at a hospital in South Carolina, where she lives, would cost $15,000. With limited insurance, she would have had to pay much of that herself. But after shopping around she found that she could have her knee repaired at a good hospital in Costa Rica for $7,400—and take a holiday, too.

Just a decade ago, stories like hers seemed to point to the future of health care. If a person could save thousands by shopping in the global health market, the reasoning went, insurers and governments could save billions. A knee replacement costs $34,000 in America, but just $19,200 in Singapore, $11,500 in Thailand and $9,500 in Costa Rica, according to Patients Beyond Borders, a consultancy. Even within Europe savings are to be found: a hip replacement is $4,000 cheaper in Spain than in Britain.

In the mid-2000s American insurers set out to find these savings by touring foreign private hospitals. They found that many were as good as their rich-world counterparts, and far cheaper. A big shake-up seemed likely. In 2008 Deloitte predicted an “explosive” boom in medical tourism, saying that the number of Americans going abroad for health care would grow more than tenfold by 2012.

It did not happen. Poor data were part of the problem: whereas Deloitte counted 750,000 American medical tourists in 2007, McKinsey, another consultancy, found at most 10,000 a year later. It is generally agreed that the number of medical tourists has grown since then—Thailand’s Bumrungrad hospital, which is popular with foreign patients, reports “steady growth”. But the data are still fuzzy. Patients Beyond Borders estimates that as many as 12m people globally now travel for care, perhaps 1m of them Americans. Industry insiders admit that growth has not matched the initial heady expectations.

Patient interest also turned out to be lower than predicted. Though some patients in the rich world seek out deals, most receive adequate health care at a manageable price and would prefer to stay at home. Potential savings are often insufficient to trump concerns about quality and the lack of recourse if something goes wrong. In 2008 Hannaford, an American supermarket chain, offered to pay the full cost of hip and knee replacements for its employees, including travel and patients’ usual share—provided they would go to Singapore. None took up the offer.

The predicted growth depended on medical tourism evolving from an individual pursuit to a cost-saving measure embraced by insurers and governments. But without reliable projections, insurers were reluctant to invest in the idea, says Ruben Toral, a health-care consultant. And cooler measures of the size of the opportunity dimmed their ardour. In 2009 Arnold Milstein of Stanford University estimated that less than 2% of spending by American insurers went on the kind of non-urgent procedures that might be moved abroad.

The legwork required also turned out to be formidable. Insurers had to choose foreign hospitals, negotiate contracts and malpractice insurance, and arrange follow-up care with American providers. They also risked upsetting the locals who would continue to take most of their custom. By the time the battle over Obamacare distracted them from contemplating transnational forays, most seemed to have concluded that they would not be worthwhile anyway. Companion Global Health Care, a subsidiary of Blue Cross Blue Shield, is the only big medical-tourism offshoot of an American insurer.

Governments have shown a similar lack of enthusiasm, perhaps because state promotion of medical tourism is usually seen as an admission of policy failure. In 2002 Britain allowed patients facing long waits to seek treatment elsewhere in Europe. Liam Fox, the shadow health secretary at the time, called the decision “humiliating” and criticised the government for not spending more at home. In Germany patient advocates blame government stinginess for the fact that some retired people choose, for reasons of cost, to live in eastern European care homes. Overall, only 1% of public health-care spending in Europe now crosses borders.

But the mere possibility of medical tourism is starting to change health care in unexpected ways. The biggest gains have gone not to patients, insurers or governments, but to hospitals, which have calculated that they could win more business by reversing the trend and going abroad to find patients. America’s Cleveland Clinic will open a branch in Abu Dhabi next year. (It already manages Sheikh Khalifa Medical City, a 750-bed hospital in Abu Dhabi.) Singapore’s Parkway Health has set up hospitals across Asia. India’s Apollo Hospitals, a chain of private hospitals, has a branch in Mauritius.

And though American firms and insurers have mostly stopped scouring the globe for bargains, some have negotiated bulk rates with top-notch hospitals at home. Lowes, a home-improvement firm, offers workers all around the country in need of cardiac care the option of going to the Cleveland Clinic in Ohio. PepsiCo, a food giant, made a deal with Johns Hopkins in Maryland. Other firms are said to be working on similar schemes. The future of medical tourism may be domestic rather than long-haul.