Judges hearing an appeal against the conviction of the so-called "Lady in the Lake" murderer will give their ruling at a later date.
Gordon Park was found guilty of killing his wife Carol, whose body was found in Coniston Water in the Lake District 21 years after she disappeared in 1976.
Park always maintained his innocence and hanged himself in prison on his 66th birthday in 2010.
The posthumous appeal was brought by Park's son Jeremy.
It was referred to the Court of Appeal by the Criminal Cases Review Commission which investigates possible miscarriages of justice.
The court heard that evidence the prosecution failed to share in Park's trial cast doubt on his conviction, making it unsafe.
But Crown Prosecution Service (CPS) lawyers contend there was "compelling" evidence against Park and his conviction was therefore safe.
Mrs Park, 30, went missing from Leece, near Barrow-in-Furness in Cumbria, in 1976.
Her husband claimed he thought she had gone to live with another man but was arrested and charged with her murder.
The case against him was dropped in 1998 but fresh evidence lead to a trial in 2005, at which he was found guilty.
Dame Victoria Sharp, one of three judges hearing the appeal, said they had reserved their judgement and would give a ruling at a later date.