The right to a jury trial is a pillar of America’s justice system, enshrined in the Constitution from a tradition dating back more than 1,000 years. But according to a report in the Wall Street Journal, the problem these days is making sure jurors stay awake.

Last week, federal judges in two New York trials – one involving charges of sanctions evasion, the other concerning allegations of corruption in international soccer – dismissed jurors who were dozing off.

In a typical criminal trial, 12 jurors in a boxed area listen for hours at a time to testimony, with a few breaks and a lunch hour. Some trials last several months.

During jury selection, the judge and lawyers interview prospective jurors to find biases, including questions about hobbies, news sources and other topics. Lawyers say they watch for prospects already napping during jury selection. When lawyers see a slumbering juror, “it is a total blow to the ego,” says Sarah Coyne, a former federal prosecutor and now a partner at Weil Gotshal & Manges LLP.

There are no concrete rules for when a judge should dismiss a juror for sleeping. Lawyers say it depends how long they were napping and whether they snoozed through crucial testimony.

In one current trial, Manhattan federal prosecutors are seeking to convince a jury that a Turkish banker is guilty of helping Iran evade U.S. sanctions. The testimony has focused on emails, spreadsheets and wiretapped calls – mostly in Turkish and translated by a live interpreter. The alleged scheme is so complex prosecutors asked one witness to draw the banks and front companies involved on a large sheet of paper. By the end, the witness had drawn a maze of boxes connected by multicolored lines and arrows to indicate the money flow.

One juror was visibly asleep throughout the first week, his head propped in his hand or rolled into his chest. Occasionally, he awoke to sip water or jot notes before resuming his nap. His eyes were closed during much of the government’s most important witness testimony. Late last week, U.S. District Judge Richard Berman dismissed the juror, telling the court he was “really sound asleep – not just dozing.” Judge Berman said when the juror was asked during jury selection what he did in his spare time, the juror said sleep. “He seemed like a very nice fellow,” Judge Berman added.

In Brooklyn federal court last week, U.S. District Judge Pamela Chen addressed a somnolent juror in the trial of three former South American soccer officials accused of corruption. “And as I am speaking to you, you are yawning,” Judge Chen said, telling the juror that he seemed to be asleep and struggling to stay alert. The juror collected his backpack, beanie and glasses and was excused.

Veteran attorneys have strategies to combat lethargy: Ask the judge to take a break before an important witness; place less-exciting testimony in the morning, not during the post-lunch food coma; walk close to the jury box and speak loudly. Judges may make eye contact with a juror next to a sleeper and motion to elbow that person awake. The government and defense are generally careful not to call out a sleeper in open court, to avoid embarrassment and turning the juror against one side.

Former prosecutors say jurors may suffer shock when sitting through a trial for the first time and realizing it is much slower paced than trials on shows such as “Law & Order.” “If you’re a criminal-defense lawyer,” says Joshua Dubin, a New York jury consultant and defense lawyer, “you pray the jurors fall asleep during the government’s case and wake up during the cross-examination.”