(CNN) -- Italy's supreme court on Tuesday explained its earlier ruling that American Amanda Knox be retried in the 2007 death of her roommate, saying the jury that acquitted her didn't consider all the evidence, and that discrepancies in testimony need to be answered.
The high court also said evidence could support prosecutors' initial argument -- that Meredith Kercher was killed in a twisted sex misadventure game at Kercher and Knox's home in Italy, the high court said, according to Italian news agency ANSA.
The appeals court jury that acquitted Knox and her ex-boyfriend, Raffaele Sollecito, in 2011 "neglected significant evidence" and theories, the high court said in a 74-page explanation.
Knox and Sollecito's retrial, which could start as soon as the fall, should examine discrepancies in testimony, the high court said. These include differing witness accounts of when screaming could be heard from the home, ANSA reported.
The high court overturned the acquittals in March, but withheld its full reasoning until Tuesday.
Kercher, a 21-year-old British exchange student, was found stabbed to death in November 2007 in the villa she rented with Knox, then 20, in the central Italian university town of Perugia.
Knox and Sollecito were arrested that year and convicted in 2009 of murder in Kercher's death, but the jury overturned the conviction in 2011. Knox then returned to her home city of Seattle, Washington.
In legal paperwork published in December 2011, the judge in the case wrote that the jury had cleared the pair of murder for lack of evidence proving they were guilty.
Another man, Ivorian drifter Rudy Guede, was convicted separately of Kercher's killing. Guede admitted having sexual relations with Kercher but denied killing her.
Francesco Maresca, attorney for Kercher's family, appeared satisfied after reading the high court's reasoning Tuesday.
The ruling "represents a very harsh judgment of the appeal trial," Maresca said.
An attorney for Knox said that he respects the ruling but he doesn't agree with it. The high court, he said, was supposed to consider only the legitimacy of the appeal but instead attempted to re-examine the whole case.
"This means that we are going to do again a trial that has already been done, a trial in which there is no clear evidence," attorney Carlo Della Vedova said.
Knox may be ordered to return to Italy for the retrial. If she refuses, the Italian government could appeal to the U.S. government for her extradition. But even if it does, it's not clear whether the United States would extradite her.
When asked Tuesday if Knox would return to Italy to face the new trial, Della Vedova replied: "Would you send your kid back?"