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 didn't 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. Sollecito also served four years of his 25-year sentence.

The bar owner, Diya "Patrick" Lumumba, showed up at the trial Monday, saying he did so to underline the damage he suffered from Knox's false accusations. "I say the same thing I said six years ago. I think she is guilty, and that is why she slandered me," Lumumba told reporters.

Knox's conviction for slandering Lumumba has been confirmed by the high court, but it asked the Florence appeals court to examine whether to reinstate an aggravating circumstance that Knox lied to derail the investigation and protect herself from becoming a murder suspect.

Meanwhile, the trials have left the Kercher family without clear answers in the death of their daughter.

In a letter submitted to court, the Kercher family urged the panel to allow any additional testing requested "so that any unanswered questions can be clarified," adding: "It has been the most difficult six years of our lives and we want to be able to seek closure."

Maresca, the Kercher's family lawyer, said they still believe that all three defendants were present at the scene of the crime.

In its stunning 2011 acquittal that overturned Knox and Sollecito's convictions, a Perugia appeals court criticized virtually the prosecution's entire case. The appellate court noted that the murder weapon was never found, said that the DNA tests were faulty, and that prosecutors provided no murder motive.

Yet the Court of Cassation ruling was likewise strident, criticizing the appeals court ruling and saying it "openly collides with objective facts of the case."

The high court said the appellate judges had ignored some evidence, considered other evidence insufficiently and undervalued the fact that Knox had initially accused a man of committing the crime who had nothing to do with it.