Though the number of international students applying to American graduate schools grew last year, it still hasn’t reached pre-Sept. 11 levels, prompting concern at Harvard over the effect of increased competition from other schools.

A recent study by the Council of Graduate Schools found an 8 percent rise in the number of international applicants, but that gain pales in comparison to last year’s 12 percent increase.

Outgoing Dean of the Graduate School of Arts and Sciences Theda Skocpol said Harvard’s numbers have “bounced back” from a plunge after Sept. 11, but that increase was hampered by students’ attraction to schools closer to home, as institutions outside of the U.S. have upped their recruiting efforts.

American schools experienced a heavy blow after Sept. 11, when a perception that it would be harder to get into the U.S. and a fall in the number of visas turned would-be students to other options.

“We were concerned for a couple of years after 9/11 and we still have to worry about how easy it is for the students we admit to get visas,” Skocpol said. “We’re not so much worried about the number of applicants as we are to get the very best students.”

She said she feared top students were choosing universities in their own developing home countries or being seduced by other established schools.

“It used to be that a really outstanding student wanting a research doctorate would always come to the United States,” Skocpol said. “Now they may stay home in India or China or go to United Kingdom or even Europe.”

Stuart Heiser, a spokesman for the Council of Graduate Schools, said the increasing efforts of other countries to recruit international students should serve as a wake-up call for U.S. schools. “Just in the last six months a number of countries have announced multimillion-dollar marketing campaigns to attract international students,” Heiser said, citing France, Canada, Australia, and the United Kingdom.

With increased competition from their international counterparts, graduate schools in the U.S., including Harvard are beginning to spend more resources on international recruitment.

Harvard alumni in other countries identify prospective students to the school’s Admission Office, according to Skocpol.