According to the United States Treasury, which publishes figures on expatriation, 231 Americans renounced their citizenship in 2008; the next year, 742 did. By 2016, the number hit 5,411, up 26 percent from 2015. It was roughly the same in 2017 before dropping to 3,983 last year.

Immigration lawyers said the numbers would be higher if embassies had the staff to accommodate the volume of requests. David Lesperance, a Canadian immigration lawyer living in Poland who specializes in helping American citizens expatriate, said many embassies around the world had backlogs in making appointments.

“The current reality is that an American who wants to renounce needs to first book an appointment in a processing system that has reached capacity — as evidenced by the significant backlogs in the granting of interview slots,” Mr. Lesperance said in an email. “In fact, the backlogs have grown so bad (up to and sometimes over a year) that most of the U.S. missions no longer publish the appointment date information online and haven’t been doing so since the system appeared to reach capacity a few years ago.”

Once that appointment is secured, the process seems to have sped up. Mr. Jafri said he had clients who waited over a year for the letter confirming they were no longer American citizens. Now, he said, that letter can come in two weeks.

“Somewhere in the system, the decision has been made to issue these more quickly,” he said. “We haven’t seen any slowdown in renouncing.”