FLORENCE, ITALY – The Florence Appellate Court hearing U.S. student Amanda Knox’s third trial in her roommate’s murder agreed Monday to run additional DNA tests on the presumed weapon, but rejected more than a dozen other defense requests for new testimony or evidence.

On the trial’s opening day, presiding Judge Alessandro Nencini said the court agreed to test one DNA trace not previously examined on the knife that prosecutors allege killed British student Meredith Kercher; the trace had previously been deemed too small to test.

Italy’s highest court in March ordered a new trial for Knox and her Italian co-defendant, ex-boyfriend Raffaele Sollecito, after overturning their acquittals in Kercher’s November 2007 killing. The Court of Cassation blasted the 2011 appeals court acquittal, saying it was full of “deficiencies, contradictions and illogical” conclusions.

Knox, now a 26-year-old University of Washington student in Seattle, has not returned to Italy for the current trial, nor is she compelled by law to do so. Sollecito, now 29, likewise did not attend the trial, as is permitted in Italy.

Kercher’s body was found in a pool of blood, her throat slashed, in the house she shared with Knox in Perugia, a central Italian town popular with foreign exchange students. Suspicion fell on Knox and Sollecito, who had been dating for less than a week, due to their conflicting stories and what some viewed as strange behavior by Knox.

A third man, Rudy Guede, was convicted in the slaying and is serving a 16-year term. That court found that Guede had not acted alone.

On Monday, Knox defense lawyer Carlo Dalla Vedova warned of a risk of an “infinite trial,” since the charge of murder has no statute of limitations. Sollecito’s lawyer, Giulia Bongiorno, asked the court to accept only “reliable evidence,” saying the intense media attention on the case had tainted witness testimony during the previous trials.

The Florence court agreed to only three requests, a sign that it will apply its own interpretation to reams of evidence and testimony already submitted in the previous lower court conviction and appellate court acquittal.

Besides a new DNA test on the knife found in Sollecito’s kitchen, the court also agreed to the prosecution’s request to again hear testimony from a jailed mobster, Luciano Aviello, who had accused his brother in the murder in a jailhouse discussion with Sollecito. Aviello, whose criminal convictions include defamation, is to testify Friday.

The court also accepted into evidence defense photos showing Sollecito’s fingernails bitten down at the time of his arrest, which the defense argues is proof he did not participate in what prosecutors allege was a drug-fueled sex game that turned murderous.

Kercher family lawyer Francesco Maresca ridiculed the notion that the bitten-down nails were evidence that Sollecito could not have undone a bra clasp that had a trace of his DNA. “I hold it with the fingertips without using my nails,” he said.

Knox’s protracted legal battle in Italy has made her a cause celebre in the United States and has put the Italian justice system under scrutiny. The Italian system does not include U.S. Fifth Amendment protection against a defendant being put in double jeopardy by government prosecution. Knox’s absence was noted by the court Monday.

“We refute the idea that because Amanda is not coming, that Amanda is guilty, that Amanda is using a strategy. Amanda always said she was a friend of Meredith’s. Amanda has always respected the Italian justice system,” one of Knox’s defense lawyers, Luciano Ghirga, told reporters before the trial opened.

Knox served four years of a 26-year sentence, including three years on a slander conviction for falsely accusing a Perugia bar owner in the murder, before leaving Italy a free woman after her 2011 acquittal.