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The judges are considering whether Finnegan Elder and Gabriel Natale-Hjorth understood that the two men who confronted them were police officers.
On Wednesday, Elder's defense team spent seven hours arguing that the officers were not in uniform and did not show police identification that early morning. Elder and Natale-Hjorth faced life sentences before the terms were reduced, and then Italy's highest court ordered a new trial.
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'32 Seconds: A Deadly Night in Rome'
Natale-Hjorth's defense team will make its presentation June 26, and a final decision from the court may come at a hearing scheduled for July 10.