She said the 26% fall in the number of student visas issued could ultimately prove counter-productive.
The second thing some say is that our policies on student visas will damage our universities.
Australia recently ditched its own strict policy on student visas in favour of a more welcoming approach.
Ten of those arrested are Pakistan-born nationals on student visas and one is a UK-born British national.
Many students are worried their inability to pay their fees could lead to their student visas being revoked.
There have been warnings that the high-profile restrictions on student visas are having an adverse impact on applications.
An Indian organisation which helps people get student visas has put up a massive billboard in that country.
And I have to say that, in other countries, when people come in on student visas, they're checked.
Kadyrbayev and Tazhayakov were in the United States on student visas from Kazakhstan, and spoke Russian as did Tsarnaev.
Taken together, we estimate that these proposals will cut the number of student visas issued by around 80, 000 a year.
For the many east Europeans already working in London, either on student visas or illegally, prospects have become markedly better.
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Under rules that came in last month, employers and colleges must join an official register to sponsor work or student visas.
Yet, when these students receive their graduate degrees, their student visas expire and they are forced to leave the United States.
Home Secretary Theresa May said student visas were being abused and "too many were here to work and not to study".
Tuition and travel costs are often very high, especially for students from developing nations, and student visas can be difficult to obtain and maintain.
She claimed there were 150, 000 reports about people possibly abusing student visas, which had not been checked by the UK Border Agency.
Education is another area of focus between the two countries - Britain handed out 30, 000 student visas to Indian applicants last year.
Bush said authorities would check on immigrants who enter the United States on student visas to make sure they actually attend school.
There are no official numbers, because many come to China on tourist or student visas, depending on the length of the internship.
She announced plans to cut the number of student visas by up to 80, 000 - about a quarter of the current numbers.
However, it is not yet known whether any of the suspects arrested on Wednesday applied for their overseas student visas after September 2007.
They were already in federal custody on suspicion of violating the terms of their student visas when they were charged in the bombings case.
Mrs May told the House of Commons that the misuse of student visas had become a "symbol of a broken and abused immigration system".
They were taken into custody last month on charges that they had violated the terms of their student visas, Kadyrbayev attorney Stahl said last week.
They were taken into custody last month on charges that they had violated the terms of their student visas, Kadyrbayev attorney Robert Stahl told CNN.
"Student visitor visas have fewer checks than full student visas and are therefore ripe for exploitation by those looking to avoid tougher checks, " he added.
The rules for student visas into the UK are to be much tougher - after fears that this route of entry is being used dishonestly.
But even islands will never catch all those with no right to be there: most illegals are visitors who overstay their tourist or student visas.
Asians, who have higher levels of education, mainly come legally on student visas or employment programs to work in sectors that are thriving, such as technology.
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