After years of legislative stalemate on immigration reform, Congress may be ready to enact a modest but important change that will loosen self-defeating restrictions on the hiring of highly skilled foreign-born workers.

Called the Fairness for High-Skilled Immigrants Act (House Resolution 3012), the bill would relax the quota system on high-tech visas so U.S. companies could hire the best-qualified foreign-born scientists and engineers regardless of their country of origin. It would be a rare step in the right direction for U.S. immigration policy.

Under current law, no more than 7 percent of the 140,000 annual permanent “green card” employment visas can be awarded to workers from any one country. That arbitrarily excludes qualified potential immigrants from China and India, each with more than 1 billion residents and thriving technology sectors. This makes no sense.

Enter H.R. 3012, sponsored by Rep. Jason Chaffetz, Utah Republican, which the House Judiciary Committee passed by a voice vote last week. The bill would eliminate the per-country limit on employment-based visas by 2015 after a three-year phase-in period. During that time, extra visas would be allocated to highly skilled workers from India and China to reduce backlogs in applications that currently stretch up to nine years.

The biggest shortcoming of the bill is that it does not increase the overall number of employment visas issued each year. Despite the ongoing jobs recession, American companies need more highly skilled workers. U.S. colleges are simply not graduating enough Americans trained in the STEM subjects — science, technology, engineering and math — to meet the needs of the nation’s high-tech sector. Immigrants are necessary to fill the gap.

Highly skilled immigrants enable American firms to create products and new ways of doing business. Immigrants co-founded some of America’s top technology companies, such as Google and Intel. A Duke University study found that a quarter of high-tech and engineering startup companies between 1995 and 2005 had immigrant co-founders. One-quarter of international patents filed from the United States are credited to foreign-born residents.

For the government, educated immigrants are pure gravy. Because of their higher salaries and low unemployment rates, they pay more in taxes than they consume in government services from Day One. According to an authoritative study by the National Research Council, each college-educated immigrant and his or her descendants represent a $198,000 fiscal gain (in net present value) for the United States. That means a boost of 50,000 such immigrants in a year would be equivalent to retiring almost $10 billion in government debt.

Many potential highly skilled immigrants graduate from American universities. According to Gordon Hanson of the University California at San Diego, in an upcoming article for the Cato Journal, foreign students account for three-fourths of doctorates awarded by U.S. universities in mathematics, computer science and engineering, three-fifths of doctorates in physical sciences, and one-half of doctorates in life sciences. “Today, the difficulty is not in attracting top foreign students to America,” Mr. Hanson writes, “but in keeping them here after they graduate.”

Yet our government limits temporary H1‑B visas to 85,000 a year for U.S. industry, a quota that often is filled months before the fiscal year begins. Permanent green-card employment visas, which also include family members of highly skilled immigrants, are capped at 140,000 a year.

America’s immigration system sends the signal to those foreign-born students with valuable skills that we would really prefer that they return to China or India to start companies and file international patents rather than remain here in the United States. And if U.S. companies cannot hire the workers they need here, they eventually will relocate their productive facilities to nations where they can.

It should not require a doctoral degree to see that allocating more green cards for highly skilled immigrants would be a big winner for the struggling American economy.