Illegal immigration on the southwest border appears to have dropped in June, according to new numbers reported Monday, signaling President Trump’s zero-tolerance policy may have been successful in changing the calculations for would-be migrants.

The Associated Press reported that the Border Patrol arrested 34,057 immigrants who illegally crossed the border last month, down from 40,344 people in May.

The numbers, which came from an unnamed government official, are still preliminary, the AP reported. But if they hold, it would be the biggest drop since the first couple of months of Mr. Trump’s tenure, when analysts say the mere fact of his election forced immigrants to change their minds about coming to the U.S.

Officials had hinted at the improved numbers in recent weeks, but have held off on commenting publicly until the data is finalized.

Mr. Trump’s zero-tolerance policy was announced in early May and began to take effect throughout the month. The goal was to change migrants’ incentives and perhaps dissuade some from making the trip.

Because migrants’ journeys often take a month or longer, analysts said the policy’s effects on would-be migrants would show in June’s numbers. It appears to be playing out as the administration hoped.

“I believe the focus on border enforcement has had an impact on the crossings,” said Kevin K. McAleenan, head of U.S. Customs and Border Protection, to reporters at the border last week.

Border Patrol arrests are judged to be a yardstick of overall illegal crossings. If arrests increase, officials think the flow of people getting through is as well. If arrests drop, they think the flow is dropping.

The zero-tolerance policy has proved to be hugely controversial. It involved prosecuting adult migrants for illegal entry — a misdemeanor — and those who have attempted to come back after previous deportations for illegal reentry, which is a felony.

Those prosecutions usually meant the migrants were jailed for at least a couple of days — and those that arrived with children had to be separated, because federal jails don’t have facilities for families. The separations sparked a massive outcry from Democrats and Republicans, religious leaders, celebrities, business groups and immigrant-rights activists.

Mr. Trump last month signed an executive order ending new family separations, though his administration is still struggling to reunite more than 2,000 children who’d previously been separated from their parents.

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