“It’s insane and has been driving everybody nuts for years,” said one student from a top 20 law school who had three interviews in New York that day, and three others across the Midwest this week. “But I don’t really see any way to fix it.”

Students are willing to jump through the hoops because the jobs are so precious. A clerkship is possibly a prerequisite for one’s own judgeship someday and a ticket to a higher salary at a white-shoe law firm. And while the process has always been competitive, it has become more frenzied in the last few years as law firm jobs have dried up and young lawyers have sought shelter in the public sector.

Clerkships traditionally go to third-year law students, but now more graduates are also competing for (and getting) these positions. The recruiting restrictions officially apply only to current students, so judges can hire graduates whenever they want without being accused of cheating.

Last year 382,828 applications were filed electronically for clerkships with 874 presidentially appointed federal judges, each of whom typically hires one to three clerks each year. (Some applications were submitted in hard copy only, but those numbers are not tracked.)

Given the abundance of candidates, it might seem strange that judges compete so intensely for interviews. Federal judges, though, are frequently fighting over a very small subset of law students from a few elite schools. After all, clerks are hired not only to research and write, but in some cases also to improve their bosses’ career prospects.

“There are some judges who like to position themselves as feeders to the Supreme Court, since that’s one way that a judge can make a reputation for him or herself,” said Joan Larsen, a faculty clerkship adviser at the University of Michigan Law School. “I have had a feeder judge say to me, ‘Yes, Joan, I’m sure he would be a great clerk, but I can’t send him upstairs.’ ” By 10 a.m. that Thursday, the official starting time for interviews, students were reduced to begging for positions in 2013. At least one judge was interviewing candidates for jobs in 2014.

No matter how far in advance an offer comes, schools pressure students to never, ever turn it down or even ask for time to consider it. Hesitating — let alone declining — is considered disrespectful, if not insulting, and can damage an entire law school’s reputation in the clerkship market.