President-elect Donald Trump has a known tendency to agree with the last person he spoke to. By naming fast-food CEO Andy Puzder as his nominee for secretary of labor, Trump is guaranteeing that at least one of the people speaking to him will be an advocate for Trump to flip-flop on his signature issue of immigration.

As an executive in a low-wage industry dominated by “low-skilled” workers (many of them immigrants, and often unauthorized immigrants), Puzder has been an outspoken supporter of low-skilled immigration to the US — and of immigration reform that would legalize unauthorized immigrants who are already here.

To some observers who were hoping for Trump to follow through on his promises, like David Frum of the Atlantic, this is proof of an enormous betrayal.

Let’s absorb the magnitude of the Pudzer appointment. Trump’s signature issue was immigration restriction. Number 1. — David Frum (@davidfrum) December 8, 2016

He slammed hard the Bush family in general and Jeb Bush in particular as weak and low energy on immigration. — David Frum (@davidfrum) December 8, 2016

And the person Trump names to head Labor? Perhaps the most outspoken advocate of Bush-style immigration policy in US business community! — David Frum (@davidfrum) December 8, 2016

Basically the Trump administration is a giant prank on Trump voters. — David Frum (@davidfrum) December 8, 2016

Frum shouldn’t give up all hope quite so easily. There are certainly other Trump appointees who have every interest in cracking down on unauthorized immigrants — and some of them, like attorney general nominee Jeff Sessions, will have more power than Puzder.

But the fact that Puzder is in the Cabinet at all (and in charge of a department that could have been mustered in service of an immigration crackdown) is an indication that Trump’s administration is not going to be as single-minded on his signature issue as his supporters hoped and opponents feared.

Puzder is a leading member of the GOP’s pro-immigrant wing — which Trump ran, and won, against

In early 2015 (before Trump entered the race), Puzder participated in a press call warning the Republican candidates for president to follow Jeb Bush’s “lead” on immigration. “People vote with their hearts ... our values dictate we should be the party of immigration reform,” he said.

By pretty much any measure, this attitude was totally repudiated in the GOP primary by Trump and his supporters. Trump mocked Bush mercilessly for calling unauthorized immigration an “act of love,” and his own characterizations of immigrants tended to focus on their potential to kill American citizens. And many Republican voters — voting with their hearts — sided with Trump.

But Puzder’s feelings about unauthorized immigrants are much more Bushian than Trumpian.

In a 2013 panel hosted by the American Enterprise Institute, as Frum pointed out on Twitter, Puzder said that immigrant workers were often more grateful for their jobs than native ones — an attitude that contrasts starkly with Trump’s crusade against companies that “replace” native workers with non-native ones so they can pay lower wages.

And during the 2015 call, Puzder expressed sympathy for unauthorized workers who “live in fear of being deported, losing what they've built and being separated from their families."

Trump has made that fear much more widespread and much more palpable for millions of immigrants. And Andy Puzder is now in a position to try to impede Trump (and Sessions) from using the full power of the federal government to enforce immigration law.

Puzder’s nomination is an opportunity cost for immigration hawks

Trump’s labor secretary won’t be the most important person in implementing his immigration agenda, but he’s arguably in the top five.

Enforcing immigration laws — even laws against working in the US illegally or hiring someone without authorization — is primarily the job of the Department of Homeland Security and the Department of Justice. Trump has already appointed immigration hawk Jeff Sessions to be attorney general; Kansas Secretary of State Kris Kobach is rumored to be in line for deputy secretary at DHS.

Appointing Puzder to Labor is an opportunity cost for the hard-liners: a choice that could deprive them of some of the tools they might have if the head of Trump’s Department of Labor saw the job as a way to go after immigrant workers and those who employ them.

Because unauthorized immigrants often work in low-wage industries and are often paid less than minimum wage, for example, there’s an argument that Department of Labor wage investigations are an indirect way of enforcing immigration law — and it’s certainly possible that a secretary of labor could make that indirect way more direct by targeting companies known to employ unauthorized workers. (Department of Labor offices have also been known to assist DHS and US attorneys in investigations against companies for hiring illegal workers.)

Arguably even more important, though, is the role Labor plays in regulating legal immigration through work visas. The Department of Labor is responsible for certifying that employers who want to hire foreign workers are complying with federal law — that they’re making an effort to recruit Americans first, for example, and not just using work visas as a way to pay workers less than they’d have to pay US citizens.

Trump (and Sessions) has made a point of attacking companies like Disney accused of replacing native workers with H-1B visa holders (for “skilled” workers) and forcing the natives to train their own replacements. That’s a violation of the terms of the H-1B — and it’s the sort of thing the Department of Labor is tasked with preventing and investigating.

Puzder’s role at Labor may matter less than as a voice in Trump’s Cabinet

There isn’t much that Puzder can do within the Department of Labor to prevent other Cabinet departments from going after immigrants. (The Department of Homeland Security could crack down on H-1B employers by simply granting fewer visas, for example.) But it’s possible, given what we know about the president-elect, that Puzder will have an influence within the administration that outstrips his own jurisdiction.

Donald Trump’s own rhetoric on immigration isn’t nearly as consistently hard-line as his stated policies. His campaign papers may have targeted H-1B visas, but he’s said that he loves legal immigration and wants a “big, beautiful door” in his big, beautiful wall. He may have promised to undo President Obama’s Deferred Action for Childhood Arrivals program, which protects certain unauthorized immigrants from deportation, but he recently told Time magazine that many beneficiaries were “good students” with “wonderful jobs” — and that he’d “work something out.”

To a certain extent, this simply doesn’t matter; what matters are the views of the people Trump is choosing to actually implement policy. But the more ambivalent Trump is about immigration, the less interested he might be in putting energy into an immigration crackdown — and, arguably more importantly, the less inclined he might be to spout the sort of rhetoric that has millions of immigrants currently terrified.

It depends greatly on who has Trump’s ear. For the most part, throughout the campaign, that’s been Sessions. But if Puzder is in the room, he may be able to have enough conversations with Trump that — at least some of the time — the last person Trump has spoken to will be someone who has a record of sympathizing with unauthorized immigrants.