The Trump administration issued a new rule on Thursday instructing United States consular officials to deny pregnant women visas unless they can prove “to the satisfaction of the consular officer” either that they are not traveling to the U.S. to give birth, or that they have a legitimate medical reason to give birth in the country.

The administration says the new provision is an attempt to cut down on what’s known as “birth tourism,” or when women come to the U.S. specifically to give birth so that their children gain American citizenship. But critics say the new rule may be deeply flawed.

One problem is that it relies on U.S. consular officials, who likely have no medical training, to review the evidence pregnant women provide and determine whether they have a legitimate medical reason to give birth in the U.S. “The fact that they’re trying to charge immigration officers, who have no medical background, with adjudicating people’s pregnancies” is very concerning, says Carolyn Sufrin, a doctor and a fellow with the American College of Obstetricians and Gynecologists.

If a consular officer believes the visa applicant could receive similar treatment in her home country, or in a country that’s geographically closer to the U.S., he or she may deny the woman’s application. If that happens, the woman can’t appeal the decision, explains Leon Fresco, an immigration attorney who was the primary drafter of the Senate’s immigration reform bill in 2013.If a consular officer denies your visa on the grounds that he believes “you’re going to commit birth tourism, and you say are not, you cannot file a lawsuit where a judge says, ‘I agree. No. You’re not,’” Fresco says. Applicants whose visas are denied can try to apply again.

Louise King, a doctor and the director of reproductive bioethics at the Harvard Medical School Center for Bioethics, says the new rule could have a “pretty detrimental impact” on pregnant women who require medical treatment, especially since the new rule could delay those who need care entering the U.S.

But, Fresco says, the actual impact of the new provision is as yet unclear. It could be “extremely large or extremely narrow,” depending on how individual State Department officials choose to interpret and implement it. “It’s completely left to the viewpoint of the adjudicator,” he says.

The new rule instructs consular officers to deny a visa to any pregnant woman seeking to give birth in the U.S. unless she can overcome a burden of proof. She must convince a consular officer that she has a legitimate medical need to give birth in the U.S. and that she cannot receive that care near her home country. She must also prove that she has arranged for her medical treatment, and that she has the means to pay for it, as well as “all incidental expenses, including transportation and living expenses.”

In other words, pregnant women must “overcome the presumption that they are traveling to the U.S. to give birth,” says Theresa Cardinal Brown, the director of immigration and cross-border policy at the Bipartisan Policy Center.

Sonia Canzater, a senior associate at the O’Neill Institute for National and Global Health Law at Georgetown University Law Center, tells TIME that while she has “concerns about the broad range of discretion that is left basically to these [officials],” she remains “cautiously optimistic.” If officials follow way the rule is written, she says, women with legitimate medical needs will receive visas. Women have usually begun arranging their care before they come to the U.S. and can show that documentation to officials, Canzater says.

Traveling to the U.S. for the explicit purpose of giving birth was not previously banned, Canzater adds. In fact, “for the purpose of giving birth” was sometimes included in women’s visa applications. “Birth tourism” is most common among women from Russia, China and Nigeria and has become a sort of “industry” in recent years, especially among the wealthy, according to Canzater.

But it’s unclear how common “birth tourism” actually is. In a press briefing, a State Department official estimated that “thousands of children” are born in the U.S. to people on visitor visas each year, but exact numbers are not readily available. Millions of visitor visas are issued every year.

The rule will not affect people coming from 39 countries that are included in the U.S.’s Visa Waiver Program, which allows citizens from those countries to visit the U.S. for brief periods of time without visas. “So then this would be discriminatorily applied to certain women as opposed to other women,” King of Harvard’s Bioethics Program says.

Brown of the Bipartisan Policy Center points out that the rule, even enforced strongly, would do an imperfect job of cracking down on birth tourism. Many visitors receive visas that expire after decade, so they could feasibly apply for a visitor visa, get pregnant, then come to the U.S. to give birth. U.S. Customs and Border Protection has not issued any guidance on the rule, and the new rule explicitly says it’s not changing any Department of Homeland Security standards of admission.

Ali Noorani, the executive director of the immigrant advocacy organization the National Immigration Forum, says one problem about the rule is that it sends an ugly message. It “continues to advance a narrative by the administration,” he says, “that children of immigrant parents are not as good as children of parents from the U.S.”

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Write to Madeleine Carlisle at madeleine.carlisle@time.com.