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The agency’s new strategy, introduced in Tucson last year and later extended to the entire border, relies on tougher punishments that were rolled out in recent years. One calls for jail for up to six months and another one buses migrants to cities hundreds of miles away to be deported there.

The one-way flights to Mexico City were aimed at first-time offenders and families. They were always voluntary and Mr. Allen said about 70 percent declined when they were introduced. But, as jail time and other punishments became more common, migrants increasingly jumped at the opportunity.

Without the flights, the Border Patrol is relying more on other punishments. It sends 70 people to federal court in downtown Tucson each weekday to face jail time. Deportation buses head east daily to Del Rio, Texas, and, when there are enough people to fill the seats, west to San Diego or Calexico, Calif.

Mr. Allen said Border Patrol data shows migrants who took the flights were less likely to be found again crossing the border illegally, though the agency has faced criticism for failing to release evidence of whether its tougher punishments are working.