In the wake of Tuesday's U.S. Supreme Court ruling striking down Florida's death penalty sentencing process, the state's Republican-controlled legislature is exploring ways to reform that process.

The legislature is meeting right now for the annual 60-day session in Tallahassee.

The high court invalidated Florida's law granting judges, not juries, final authority to mete out sentences in capital cases. The system, the majority opinion said, is inconsistent with the constitutional right to trial by impartial jury.

"I think we do need to put this in the hands of the jury and we must provide a structure and a process by which the jury properly deliberates," said Sen. Thad Altman (R-Melbourne), the sponsor of a measure to hand sentencing power to juries and require a unanimous verdict in capital cases. "I think it's a good starting point in dealing with the U.S. Supreme Court decision."

Other Republican legislators, however, are less willing to pursue expansive reform of Florida's death penalty process. The chairman of the House Criminal Justice Subcommittee plans to introduce narrowly-tailored legislation that satisfies the Supreme Court's call for jury-dictated sentencing. His counterpart in the Senate, meanwhile, has no plans to pursue any type of death penalty reform.

While a fundamental rethinking of the state's decades-old death penalty is unlikely this year, some Democratic lawmakers predict the Supreme Court ruling will serve as a catalyst for broader reform.

"One of the tragedies, I think, that's unfolding before us is, how many people have their lives been taken by a state, and it's found that they didn't commit the crime? That's a big deal and that's why we need to take these things very seriously," said House Minority Leader Mark Pafford (D-West Palm Beach).