Want an H-1B visa to work temporarily in the U.S. starting this fall? You still have a pretty good shot if an employer is willing to file a petition for you. The U.S. still has about 20,000 visas available for fiscal 2010.

It's been nearly four months since the U.S. began accepting from employers H-1B visa petitions for IT and other professionals for temporary jobs starting in fiscal 2010, which begins Oct. 1. The weak economy continues to dampen demand of the visa most popular among employers seeking IT workers.

Since the U.S. began accepting fiscal 2010 visa petitions on April 1, the U.S. has hit about two-thirds of the annual cap on general H-1B visas. At last count, as of July 10, U.S. Citizenship and Immigration Services had received 44,900 H-1B visa petitions toward the congressionally mandated annual cap of 65,000.

However, the demand by employers for more highly educated H-1B visa workers is apparently stronger. By the end of April, the U.S. had reached the cap of 20,000 H-1B visa exemptions for foreign workers with advanced degrees -- including masters and PhDs -- from U.S. schools.

But because the general category H-1B visa cap of 65,000 hasn't been hit yet, USCIS will continue to accept advanced degree as well as general H-1B petitions until the agency reaches the statutory limit on all H-1Bs.

The fact that it is mid-summer and the H-1B visa cap hasn't been reach yet is startling when contrasting this year's demand to the last couple of years, when USCIS received enough petitions to hit the combined 85,000 limit within days of accepting the applications in April.

But with the economy still sputtering, few expected demand for H-1B visas to be as robust this year as in the past.