Police have indicated that Joanna Yeates may have been murdered at home after revealing her boots and coat were left in her flat.
Detectives also said that the murdered architect was missing a sock when her body was found near Bristol, raising the possiblity that the killer may have taken it as a souvenir of his crime.
Detective Chief Inspector Phil Jones, who is leading the inquiry, said the sock was a long, ski-style size five. A pizza bought by Miss Yeates on her way home has also disappeared and could also have been removed by the killer.
At a press conference, where DCI Jones held up a sock similar to the one Joanna was wearing, he said: "When Jo was found on Christmas Day morning she was fully clothed. She wasn't wearing her jacket. She wasn't wearing her boots and she was only wearing one sock.
"The jacket and the boots have been found at her home address. That would indicate that Jo had returned home. However at this present time the sock has not been found."
DCI Jones urged anyone with new information to come forward as police investigating the murder are coming under growing criticism of their handling of the case.
Detectives admit that they still do not know where and when the landscape architect died and at what stage her body was dumped by the roadside three miles from her flat in Bristol.
Miss Yeates was last seen on the evening of Friday December 17 after she had been drinking with colleagues in the Ram pub in Park Street.
The 25-year-old's snow-covered body was found on Christmas morning by a couple walking their dogs just three miles from her home in the Clifton area of Bristol. She had been strangled.
Police have said there was nothing to suggest the murderer was a serial killer or that people should be unduly worried but have warned women not to walk home alone.
Impatience at no sign of a breakthrough in the investigation is growing in Bristol.
Trevor Blythe, Clifton ward councillor, told The Guardian: "People are afraid to go out at night and are taking extra precautions at home. Clearly the person or people who did this are still around.
"The police don't appear to have any leads at all. Everyone wants it resolved so we can get back to normal life. It could well be that the perpetrator knew the victim so it doesn't seem like a serial killer – but we just don't know."
An Avon and Somerset police authority member, who asked not to be named, told the paper it was "worrying" that the police did not appear close to finding the murderer.
Detectives have launched a national campaign on Facebook to appeal for witnesses.
Avon and Somerset Police have placed an advert on the social networking site, appealing for help in catching the landscape architect's killer.
Detective Chief Inspector Phil Jones, who is leading the murder investigation, said: "The majority of people these days are spending time on Facebook and other social networking sites.
"This has become part of everyday routine for many people.
"This advert allows us to point people to special features on our website with all the latest information, it allows them to contact the incident room direct online rather than calling in.
"I would once again urge anyone who may have not contacted my team and may have information that could help this inquiry to contact us. Let us decide if this information is significant."
Crime scene investigators remain at Miss Yeates's flat, using advanced forensic techniques to examine the scene.
There was a sign outside the building in Canynge Road saying "Do not enter, dangerous chemicals."
Avon and Somerset Police have successfully used Facebook in several other high-profile cases.
It is a more cost-effective method than poster campaigns and mass leaflet distribution and, due to the viral nature of Facebook, can be shared much wider.
Scott Fulton, head of e-services for the force, said: "Social media is growing rapidly and has become a daily factor in most people's routine.
"On this inquiry alone we have had shares of the story from the force's Facebook page of 24,220. Additionally there have been over 63,000 views of the news updates on our website, a further 18,000 on the dedicated Jo page and over 70,000 views of the CCTV clips on our YouTube channel.
"Through the website we have had 260 inbound messages to the incident room. Anyone can send information to the team this way via avonandsomerset.police.uk/jo.
"We have been very pleased with information received via these channels on this investigation and we hope this advert will encourage even more people to come forward.