A police computer expert has told the Angelika Kluk trial that "low-grade" pornographic images were discovered on her married boyfriend's computer.
Martin MacAskill was dating Angelika at the time of her death
Andrew Calman said no such material had been found on Angelika's computer or on one belonging to St Patrick's church.
However, he said it was possible that evidence of sexually explicit names on an internet contact list could have been deleted or not been discovered.
Peter Tobin, 60, denies raping and murdering Miss Kluk in September 2006.
Advocate depute Dorothy Bain, prosecuting, asked Mr Calman - a police computer investigations and security officer - about Angelika's computer.
She said: "Were you able to determine where she had browsed and whether she had accessed any pornography?"
He replied: "There was no pornography in those two items."
Mr Calman, who worked in a police computer forensic unit, said that as well as examining a laptop and memory stick from Miss Kluk, he also looked at a laptop, hard drive and flash pen belonging to her married lover, Martin MacAskill.
He described how investigators had found explicit images on computing equipment belonging to Mr MacAskill.
He said: "There was a small quantity of pornography on those three items.
"I would describe them as general pornographic material, there was no evidence of fetishes or the like."
During detailed questioning about the police investigation into the church's computer, Mr Findlay asked if any sexually explicit usernames had been found on an MSN Messenger contact list, specifically the name Wonderboy.
Mr Calman acknowledged that the name Wonderboy had been mentioned to police, but said nothing had been found.
Mr Findlay asked: "If someone comes in and gives evidence that they saw on the church computer, via the internet on MSN Messenger using Wonderboy, a list of sexually explicit names, foreign, Polish names - could they be telling the truth?"
"That's possible, yes," Mr Calman answered.
Miss Kluk stayed at St Patrick's Church in the Anderston area of Glasgow last summer during a working holiday in Scotland. Her last contact with Mr MacAskill was on the afternoon of Sunday, 24 September.
Her bloodstained body was discovered the following Friday under a hatch in the church floor, near the confessional box.
Mr Tobin denies murder, attempting to defeat the ends of justice, attempting to pervert the course of justice and breach of the peace.
He is accused of attacking Miss Kluk at the church, or elsewhere, between 24 and 29 September.
Mr Tobin also denies rape and claims he had sex with Miss Kluk with her consent.