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Also, more airlines are unlikely to start offering the benefits of adoption fares, since international adoptions have decreased as host countries adopt stricter adoption accreditation policies, said Mr. DiFilipo.

International adoptions decreased by about 9 percent in 2006 from 2005, according to the State Department, which keeps track of the number of immigrant visas issued to orphans traveling to the United States.

The United States issued 20,679 such visas last year, according to State Department figures. International adoptions peaked in 2004, when 22,884 visas were issued to orphans.

The flexibility of adoption fares remains a useful tool for the estimated 20,000 international adopters each year. But they are not the only option, Mr. DiFilipo said.

“Sometimes what we’ve seen is that you can go online and get a cheaper fare than an adoption rate but without the benefits,” Mr. DiFilipo said. “You just can’t go in and look at the adoption fare.”