A post-mortem examination into the death of Bristol landscape architect Joanna Yeates found she was strangled.
The 25-year-old's snow-covered body was discovered by a couple out walking their dogs in Longwood Lane, Failand, on Christmas Day.
Miss Yeates, from Clifton, had not been seen since she was filmed on CCTV at a Tesco store on 17 December.
Police said a murder investigation was under way. The family have formally identified her body.
Det Ch Insp Phil Jones told a news conference the post-mortem results had shown she had been dead for "several days before being discovered".
"The investigation is now a murder investigation, " he said.
"The post mortem examination has taken longer than usual, due to the frozen condition of her body.
"The cause of death was compression of the neck - in other words, strangulation."
He appealed for further information to help their investigation and said they were keeping an open mind as to whether the killer was known to Miss Yeates.
He confirmed boyfriend Greg Reardon was a witness and not a suspect.
His laptop and mobile telephone have been examined by detectives but officers have stressed that this was a routine procedure in such inquiries.
Det Ch Insp Jones appealed for anyone with information to come forward.
He said: "Somebody out there is holding the vital piece of information we need to provide Joanna's family with the answers they need and they want."
Cameras recording movements across Clifton Suspension Bridge - which links the area where the body was found with Miss Yeates's flat - are already being studied.
Miss Yeates's parents, David and Teresa, her brother Chris, and Mr Reardon have visited the scene where her body was found near Long Ashton Golf Club and laid flowers.
Police have appealed for information which may help them fill in the gap between Miss Yeates's disappearance and the discovery of her body.
She is thought to have returned to the flat she shared with Mr Reardon, 27, on the evening of 17 December.
Her keys, mobile phone, purse and coat had been left behind at their flat.
Forensic examiners said there was no sign of a forced entry or a struggle at the flat.
Mr Reardon was in Sheffield visiting family for the weekend and reported her missing to police when he returned home two days later.
Police said she had been to the Ram pub in Bristol's Park Street the night she disappeared, but left there at about 2000 GMT.
CCTV images showed Miss Yeates visiting a Waitrose store on The Triangle, a Bargain Booze shop and then the Tesco Express store, where she bought a pizza.
A receipt for the food was found at her address, but no trace has been found of the pizza or its wrapping and detectives believe its whereabouts could hold a vital clue in the case.
Officers are also keen to hear from people who may have seen anything or anyone acting suspiciously over the past week in the Longwood Lane area.