The pools are more popular in Austria, where a company called Biotop has been designing them for residential and public use since 1986 and now installs about 50 a year, according to Peter Petrich, Biotop’s owner and the person credited with inventing the concept.

Mr. Petrich said he and his colleagues have given much consideration to why natural pools haven’t caught on in the United States and have concluded that “perhaps in Europe people have more contact with nature and life is not so clinical.”

Toni Schneeweiss of Biotop said that private pools in Austria, unlike those in the United States, generally do not require building permits, which can be harder to obtain for projects using unfamiliar technology. But it is also true that natural pools are not well known in the United States, and that it is hard to find people to build them.

For builders like Mr. Hilleary and Mr. Morse, natural pools are a side business, and mainstream pool contractors don’t seem to offer them at all. Penny Johnson, the chairwoman of the Association of Pool & Spa Professionals, an industry trade group, said she had never heard of the concept until she was asked about it for this article. She expressed skepticism about the technology. “I don’t know how plants could filter the water for bathing use,” she said, adding that in her experience outdoor pools have to be “shocked” with chemicals to kill bacteria.

Asked about safety concerns, Mr. Petrich said that the water in the natural pools his company builds meets European Union standards for bacteria levels and that the risk of swimmers becoming sick is “very low.”

One American homeowner who has such a pool, Jim Smith, a 45-year-old computer programmer who lives in a suburb of Wichita, Kan., said he learned about the pools in a sales pitch given by Mr. Hilleary at a home show in 2002. Mr. Smith and his wife, Susie, who is an avid gardener, decided to build a natural pool with a miniature waterfall, plants like hornwort and anacharis and a 40-foot recirculating stream that would run past their living room windows. (Mr. Smith said he spent about $50,000 on the pool, or $20,000 more than he estimates a standard pool would have cost; he attributed the higher cost in part to elaborate landscaping.)

The couple, who have two daughters, had a chlorinated pool at a previous home, and Mr. Smith said the transition was difficult. “It took us the first year to learn how to deal with the water,” he said, referring to the way natural pools can become overgrown with algae. “In a regular pool, you just put chlorine in and shock it.”