PRESIDENT TRUMP began his unusual news conference Thursday by announcing a new nominee for labor secretary, former Justice Department official Alexander Acosta. This was to clean up another mess of Mr. Trump’s own making: the failed nomination of restaurant-chain operator Andrew Puzder. Mr. Puzder, a strident critic of increases in the minimum wage as well as Obama administration enforcement of key labor regulations, withdrew, though not because of predictable Democratic objections to his ideology, or because of murky charges of domestic abuse levied long ago and then retracted by his ex-wife. Nor was his fatal difficulty a long delay in producing an ethics report to account for his various businesses. Rather, what ultimately cost him Republican support in the Senate was disclosure of his failure to pay required employment taxes for a domestic employee, who was also undocumented.

This was a spectacularly bad vetting job and as such raises the question of whether the choice of Mr. Acosta holds more promise. On paper, his credentials are strong: He has served as a federal prosecutor, civil rights head at the Justice Department and, for a brief time during the George W. Bush administration, member of the National Labor Relations Board. There will — and should — be questions about controversies during his career, notably a 2004 episode when, as the Justice Department’s civil rights chief, he urged a federal court to look kindly on Ohio GOP challenges to the credentials of some 23,000 African American voters.

But Mr. Acosta’s confirmation hearing needs principally to be the forum at which we get a better sense of Trump policy toward the healing but still troubled labor market. Mr. Puzder would have brought a franchise chain operator’s sensibility to the task. What is Mr. Acosta’s take on maneuvering between the unrealistic movement for a $15-an-hour minimum wage, on the one hand, and the lack of any increase in the federal minimum since 2009 on the other? The Obama administration’s expansion of overtime-pay eligibility has been blocked by a federal judge. And yet the existing standard needs an update; does Mr. Acosta favor an alternative proposal, offered by five Republican senators last year, that claims to achieve the same goal as Mr. Obama’s plan with less disruption to business?

The Senate should demand that the nominee guarantee no fiddling with the Bureau of Labor Statistics, Mr. Trump’s repeated attempts to delegitimize its unemployment data notwithstanding.

Wielding crucial but underpublicized authority over every American worker’s daily life, the secretary of labor is a key position, and it is up to Mr. Acosta to show that this president has finally figured out how to fill it.