Amanda Knox is on trial for murder. She insists on her innocence. What could she possibly to do to convince people to believe her?
Back when my primary area of interest was the psychology of deception, I had a terrific graduate student (now a professor) who wanted to answer the question of how people who are accused of a serious offence can establish their innocence. Weylin Sternglanz conducted a series of studies on that question for his dissertation. (Reference is at the end of this post.) He never studied people who were accused of murder, so we can't know for sure if his results would generalize to bad behaviors of that magnitude, but his findings are suggestive.
Sternglanz believed that people who completely deny an accusation of serious wrongdoing are not as likely to be believed as those who admit to a lesser offense. Take, for example, the case of academic cheating, as when a student is accused of copying a fellow student's answers on a test. Students who simply deny the accusation are less likely to be seen as innocent than those who say they did not personally engage in cheating but they did see someone else cheat and did not report it.
The cheating example was the basis for one of Sternglanz's studies. In another study, people described times they really were accused of serious transgressions (such as drunk driving, infidelities, plagiarizing, and engaging in nonlethal violence). In that study and one other, people adopted different strategies in their attempts to convince others (all of whom were strangers) of their innocence. The two key strategies were simply denying the accusation and admitting to a lesser offence. Others included for comparison included making a counter-accusation, offering an explanation for the accuser's suspicions, admitting to a lesser offence that had nothing to do with the accusation in question, and not responding to the accusation at all.