Illegal immigrant families are streaming across the border at record pace, according to new Border Patrol statistics released Friday morning that show more than 32,000 have been caught trying to sneak into the U.S.

That’s nearly 40 percent higher than the previous record of 2014, and it’s well more than double last year’s pace, suggesting that the government’s relaxed enforcement policies have backfired and invited a new wave of illegal crossers.

There’s somewhat better news when it comes to children traveling alone. The record pace has slackened slightly — though an uptick in March suggests that the warmer months could once again see a massive wave at the southwest border.

Homeland Security Secretary Jeh Johnson had thought he’d licked the problem two years ago, after surging manpower to the border. And indeed the numbers did drop in late 2014 and early 2015.

But the pace of both families and unaccompanied children picked up last summer, just as Mr. Johnson announced new relaxed rules for detaining illegal immigrants, and it has remained high ever since.