The Trump administration proposed a change to the H-1B program Friday that could make it harder for Indian outsourcing firms to hire workers from overseas, while helping large Bay Area tech companies bring highly skilled foreigners to their headquarters.

The rule change tinkers with the lottery that determines who gets the 85,000 H-1B visas granted to for-profit companies every year.

Currently, a person with a master’s or doctoral degree from an American college or university has better odds of receiving a visa, because they’re eligible for a lottery just for people with U.S. advanced degrees that gives out 20,000 H-1B visas. If they miss their shot, they continue on to a lottery for the remaining 65,000 slots, for which individuals with either graduate or undergraduate degrees are eligible.

The Department of Homeland Security wants to switch the order of these lotteries, it said in a notice of the proposed rule change, which would — somewhat counterintuitively — improve the odds for those highly educated workers.

Changing the order would mean more highly skilled workers would compete for the same number of visas, reducing the likelihood that people without advanced degrees win in the general lottery. Those who studied in the United States and are more likely to be brought on at high-tech companies would still have a second chance in the smaller lottery dedicated to U.S. advanced degree holders.

U.S. Citizenship and Immigration Services, the agency within the Department of Homeland Security that oversees the H-1B visa process, said that the proposed change would result in an estimated increase of up to 16 percent in the number of H-1B visa holders with U.S. advanced degrees, or about 5,000 workers.

Technology staffing companies, also known as outsourcers, are “notorious” for flooding the lottery with petitions that “may or may not be super legit,” said Doug Rand, who worked on immigration policy in the Obama administration and is now co-founder of Boundless Immigration, a tech firm that helps families navigate the process.

The lottery change could be aimed at hindering those outsourcing firms’ applications, Rand said. Three Indian firms, Tata Consultancy Services, Infosys and Wipro, have dominated H-1B applications since 2012, government data shows.

“Most of the visas are snapped up by these body shops,” said Ira Mehlman, a spokesman for the Federation for American Immigration Reform, or FAIR.

FAIR has argued that the H-1B program has strayed from its original intent to help American employers hire workers with special skills.

“It was not intended as a program to enrich foreign labor contractors,” Mehlman said.

The Information Technology Industry Council, a trade association that represents both Silicon Valley companies and Indian outsourcing firms, said it’s reviewing the policy change.

The National Association of Software and Services Companies, or Nasscom, a trade association for Indian outsourcers, did not respond to a request for comment.

The public will have 30 days to comment on the proposed rule change starting Dec. 3, when it will be officially published. That’s about half the time the department usually gives for a public comment period, according to Chad Graham, an attorney who specializes in work-based immigration at San Jose law firm Graham Adair.

In addition to the new lottery order, the department also proposed a new way for companies to enter their H-1B visa applicants into the lottery. Currently, employers have to prepare a full petition for each applicant before they’re picked. The proposed rule change would let employers register them online before the lottery, and work on their cases only if applicants are selected.

“I would say the shorter notice and comment period means they want to push it for this year,” before the April lottery, Graham said. “What you have to wonder is how likely is it that the system is going to work by they time they need it to.”

Graham said he will recommend clients prepare their full cases as they normally would. That means hiring an immigration attorney, collecting the necessary documents and preparing a package to be mailed or couriered to a USCIS facility.

Rand pointed out that the proposed rule change will be received warmly by policy observers who want to lower immigration and bring in higher quality beneficiaries.

“There’s no lack of ambition on the part of the Trump administration to radically change the legal immigration system,” he said. “It just so happens that this one is a bit more technocratic and has less exotic legal arguments.”

Melia Russell is a San Francisco Chronicle staff writer. Email: melia.russell@sfchronicle.com Twitter: @meliarobin