For example, the H-1B visa, which allows employers to hire foreigners temporarily in certain specialized fields like technology, has drawn accusations from union groups and others that companies use it to bring in lower-skilled labor.

The O-1 visa allows individuals of "extraordinary ability" to come to the United States for up to three years, and can be extended. British journalist Piers Morgan used one when he replaced Larry King on his late-night TV show, Wright said.

The EB-1 is similar, but leads to a green card and permanent residency rather than a temporary stay, with "extraordinary ability" being one of the ways to qualify - along with being an outstanding professor or researcher, or a multinational executive.

Foreign entrepreneurs have another option - the Immigrant Investor Program, or EB-5 visa - but it requires a capital investment of at least $500,000 and the creation of at least 10 full-time jobs for U.S. workers.

By contrast, no proof of personal wealth or investment in the United States is required for the O-1 or the EB-1.

There is also no cap on the number of O-1s that the government can award each year; about 12,280 were approved in 2011, U.S. Citizenship and Immigration Services said, up from 9,478 in 2006. It issued about 25,000 EB-1s last year, below their cap of 40,000.

The H-1B is much more popular. Applications hit their annual cap of 85,000 earlier this month.