The White House hailed Friday’s jobs report for May, and it did beat market expectations with a net gain of 139,000 in payrolls. But there are signs of weakness under the labor-market hood that bear watching.

The unemployment rate stayed low at 4.2% for the third straight month. Employers are holding onto their workers despite the uncertainty over tariffs. Wage gains were also healthy, rising 3.9% over the last 12 months.

The weaker news is that the jobless rate stayed the same because some 625,000 people left the job market. As a result, the labor participation rate fell 0.2% in the month, and the employment-population ratio by a highly unusual 0.3%. Some 71,000 more people were jobless in May, and Labor Department revisions showed 95,000 fewer new jobs in March and April than previously reported.

Our friend Don Luskin of Trend Macro notes another concern, which is two months in a row of shrinking foreign-born employment. Leaving aside the legal and other problems with Joe Biden ’s border failures, there’s no doubt that immigrant labor buoyed the job market over his Presidency. That seems to be going into reverse, as you’d expect with the Trump Administration’s crackdown.

In the four months of Trump II, Mr. Luskin calculates that the immigrant population has shrunk by 773,000, or 193,000 a month. Fewer immigrants mean fewer workers to fill job openings, so there will be a cost in future growth from the Trump Administration’s border closure and deportation roundups.

None of this heralds recession, but these are notes of caution for the Federal Reserve as the Open Market Committee meets this month to consider whether to resume cutting interest rates. Inflation remains above the Fed’s 2% target, though there’s little sign so far that tariffs have produced a broad-based increase in prices.

Mr. Trump keeps banging away at the Fed, which won’t help. But he can do more himself by setting aside his tariffs, or at least completing what he says will be those great trade deals. Also, support the Senate effort to make the business tax provisions in the House tax and budget bill permanent, rather than phasing out in 2028 and 2029. The May job market isn’t signaling the boom Mr. Trump promised voters.