One of two bills that would eliminate the per-country cap on green cards has been blocked in the U.S. Senate, according to a report Thursday.

The annual 7 percent cap on green cards for citizens of any one country has led to waits of many years for foreign nationals working in the U.S. on the H-1B visa and seeking permanent residency, with citizens of India waiting the longest because they dominate the H-1B system.

Under bill S386, sponsored by Sen. Mike Lee (R-Utah) and also spearheaded by co-sponsor Sen. Kamala Harris (D-CA), a maximum 85 percent of green cards could be allocated to Indian or Chinese citizens in 2020. In the second and third years, that proportion would rise to 90 percent.

The bill, called the Fairness for High-Skilled Immigrants Act and introduced in February, requires unanimous consent to be brought to the Senate floor, immigration lawyer William Stock noted on Twitter. On Thursday, Sen. David Perdue (R-GA) blocked it — for now. “I support this bill,” Perdue said. “We have some language that needs to be clarified and I still have some concerns about the impact this legislation would have on some specific industries in not only my state but in the country.” Perdue said he wanted to work with Sen. Lee to “quickly” resolve his concerns about the bill.

Earlier this year, Sen. Rand Paul (R-KY) blocked the bill, seeking a carve-out for nurses.

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Scams block some Chinese investors’ path to U.S. green cards The version blocked Thursday contained a carve-out for “shortage occupations,” according to a tweet by Migration Policy Institute analyst Julia Gelatt. The institute has projected that even if the bill passed, skilled professionals newly applying for green cards might still have to wait almost 14 years before getting one, institute analyst Sarah Pierce tweeted Thursday.

An identically named companion bill, HR1044, that originated in the House, sponsored by Congresswoman Zoe Lofgren (D-San Jose), passed the House easily in July with bipartisan support.