The man accused of her murder, John Taft, now 49, told his wife that he was at the home of Cynthia Bolshaw on the night she was killed and asked her to provide an alibi if required, Liverpool Crown Court was told.
Although police spoke to Mr Taft shortly after the murder, he was never under suspicion. Barbara Taft - who divorced Mr Taft in 1988 - did not tell police what he had told her until this year.
DNA profiling was employed to investigate Mr Taft and "everything fitted together together with a deadly logic", said Andrew Edis QC, for the prosecution. A black neglige found in Mrs Bolshaw's bedroom, where she was murdered, had traces ofsemen that matched a sample taken from Mr Taft in April.
"A murderer can escape justice for a very long time but then be discovered. No murderer can ever feel quite comfortable," Mr Edis told the jury.
Mr Taft, from Birkenhead, Merseyside, denies the murder.
Mr Edis told the court Mrs Bolshaw, a divorcee, worked at a department store and lived "the life of an attractive, single woman" at her bungalow inHeswall, Wirral. "She enjoyed the company of men and enjoyed an active sex life."
One of her lovers was Mr Taft, a double glazing salesman who had carried work out on her home. The two were seen together in easy conversation at a local pub several nights before she died, Mr Edis said.
On the night of the murder, 8 October 1983, Mrs Taft was away doing a university course.
Mrs Bolshaw arrived home from work at 6.20pm in her Toyota, which remained parked in her driveway all evening. By 4.30am, she had been strangled by someone's bare hands. She also suffered bruising to her body and face.
Mr Edis said: "There was no sign of forced entry into that house so it would appear that anyone who came to the house and did this to her was let in with her permission.
"She was found naked face down in a bath of water. But there were signs in the bedroom that she died there. She was certainly dead before she was placed in the bath."
Mr Edis said Mrs Bolshaw's Toyota was later found abandoned near a footpath which would have enabled Mr Taft to walk the seven miles to his home within a few hours, thereby throwing police off his scent.
Mr Taft had told his wife he had been at Mrs Bolshaw's to "do a foreigner" and admitted destroying the clothes he had been wearing that night.
His next-door neighbours from 1983 said they had seen him acting "very oddly" at the time, digging a hole in his garden at night by torchlight.
Mr Taft had told police - who found his business cards at Mrs Bolshaw's house - that he did not know her. However, he informed his boss that he did, asking him to corroborate his story that he had only visited Mrs Bolshaw's house to look at her windows.
During five hours of police interviews, Mr Taft would only deny his guilt and say "no comment," the court heard.
Mrs Bolshaw's son, Christopher, said his mother was a "classy woman" and a "flirtatious type". He said that her male friends included a captain in the Royal Sultan of Oman's army, an inspector in the Ugandan police, a customs officer, an oil rig worker and an American magician.
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