Supreme Court justices seemed troubled Tuesday by Florida’s unique system of imposing the death penalty, as they considered a challenge that argues the process gives judges too much power and juries too little in assigning the ultimate punishment.

The case was one of two important criminal justice issues that the court considered in a longer-than-usual session. The court also heard arguments about whether juveniles sentenced to life in prison without parole should be able to challenge those sentences, since the court has ruled that states cannot make such punishment mandatory.

But on the issue about juveniles, the justices got stuck over whether the case they had accepted from Louisiana actually gave them jurisdiction to settle the issue for the rest of the country. One option might be to accept a different case.

In the Florida death-penalty case, challengers said the state law conflicts with the Supreme Court’s decision in 2002, which said that a defendant has the right to have a jury – rather than a judge – decide whether something extraordinary about the crime makes the defendant eligible for the death penalty.

“Under Florida law, Timothy Hurst will go to his death despite the fact that a judge – not a jury – made the factual finding that rendered him eligible for death,” said Washington lawyer Seth P. Waxman.

Hurst was convicted of the 1998 murder of Cynthia Lee Harrison, his coworker at a Popeye’s Louisiana Chicken restaurant in Pensacola.

“Florida, and Florida alone,” Waxman said, has such a “muddle” of responsibilities between a judge and jury. Florida is second only to California in the number of death-row inmates, and Waxman said there are numerous reasons to think Florida’s approach is unconstitutional.