Are the Joanna detectives without a clue?

As criticism mounts, have the police missed something – or do they know more than they're saying?

Avon and Somerset Police have defended their handling of the investigation into the murder of Joanna Yeates, claiming last night that the disappearance of the 25-year-old landscape architect from Bristol had been dealt with as a murder investigation in all but name from the moment she was reported missing on 19 December.

The statement was in contrast to previous claims made by police that her disappearance had been dealt with as a vulnerable missing person case until her body was discovered on Christmas Day.

The defence came as Ms Yeates's brother Chris spoke for the first time of how he had "entered into a surreal hole of despair" and "shared the fear that my parents had that something bad had happened to her". He added: "I got to say a final emotional goodbye to Jo and the despair I had was replaced with a wave of deep sadness."

Mr Yeates thanked the public for the "tremendous amount of support" and in a moving tribute to his sister said: "She lived her life to the full and is an inspiration to me to follow one's passions." Praising the detectives' efforts, he added: "I have confidence that they will track down the person or persons responsible."

The statement came as pressure mounted on police to find her killer. Ms Yeates went missing from her home in Clifton on 17 December. She was reported missing by her boyfriend Greg Reardon two days later when he returned from a weekend away, and her snow-covered body was found in Failand, four miles away, by a couple walking their dog on Christmas Day.

A spokesman for Avon and Somerset Constabulary claimed that the case had been given the highest priority from the start: "It was designated as a high-risk missing person case immediately. We treat high-risk missing person cases the same way we would do a murder investigation. The full resources of the force were applied and the major incident room was set-up the day after."

Police have spent weeks carrying out detailed forensic examinations at the site where she was found and at Canynge Road, where she lived.

Certainly the frozen state of her body and the time that forensic tests take to complete did not help police make swift progress. The scale of the investigation is vast, with more than 1,000 different leads being followed.

Detective Chief Inspector Phil Jones, who is leading the investigation, warned last week that the inquiry could be "potentially long and complex". His boss, Chief Superintendent Jon Stratford, appealed last Friday for people to give "the investigation team the time and space they need to bring Jo's killer to justice."

In contrast to media criticism, Ms Yeates's family appear happy with the handling of the case. Her parents, David, 63, and Theresa, 58, said: "We maintain regular contact with the police, and continue to give them our support and assistance any way we can." In a statement yesterday, they added that they feared "Jo would simply be just another statistic" but have been "overwhelmed by the reactions of everybody over Jo's disappearance and subsequent murder".

Detectives are following up new leads after questioning more than 200 motorists, residents and drinkers at pubs in Bristol last Friday while retracing Ms Yeates's last-known steps.

Attempts to find a missing pizza box that she bought the night she disappeared, or any trace of a light-coloured 4x4 vehicle seen the same night on the road where her body was later found – have yet to bear fruit.

Ms Yeates's landlord, Chris Jefferies, remains the only suspect to have been arrested to date, and was bailed on New Year's Day after being questioned by police for three days. It emerged last Friday that he has spoken to friends expressing his confidence that he will be cleared.

The police continue to face questions about how the investigation has been carried out. Drains outside Ms Yeates's home and bushes on the other side of her garden wall were searched only last Thursday, and there have been claims – denied by police – that CCTV footage from privately owned cameras may have been deleted before officers had time to check them.

Detectives still do not know where and when she died, and waited 10 days after her body was found before putting an appeal on Facebook to prompt more witnesses to come forward. And last week it was a national newspaper – not the police – that released a CCTV image of Ms Yeates taken just minutes from her flat.

Anger at the levels of scrutiny that they have been under led to the police temporarily banning ITV News from press conferences last week, after a news report suggesting they were no nearer to solving the murder. The police and ITV News refused to comment yesterday.

While police maintain they are "quietly confident" of solving the case – and plan to make an appeal on BBC's Crimewatch later this month – speculation mounted last week that there may be a link with the death of 20-year-old Glenis Carruthers, who was strangled in 1974 after leaving a party in Clifton.

The parallels are striking. In both cases the crime appeared motiveless, the victims were in their 20s and were attacked at night. Both were found without shoes and neither had been sexually assaulted or suffered any significant injuries other than strangulation. The killer of Ms Carruthers has never been caught.

While the murder of Joanna Yeates has captured media attention, there are several other women who have gone missing since December and whose whereabouts remain a mystery. Nasim Akhtar, a 41-year-old mother of six from Birmingham, has not been seen since 23 December; Helen Van Duivenbode, 28, from Dorset, has been missing since 20 December; Marian Brailey-Tucker, 50, went missing from the Princess of Wales Hospital in Bridgend on Christmas Eve; and Deborah Anne Pearson, 43, a mother of four from Cumbria, has not been seen since she left her home in Thornthwaite near Keswick on 21 December.