Defence secretary John Reid is "keeping an open mind" about whether a World War I soldier shot for cowardice should be pardoned, the High Court has been told.
Private Harry Farr was one of 306 British soldiers shot for cowardice
Lawyers for the family of Private Harry Farr, 25, from 1st Battalion West Yorkshire Regiment, say he had shell shock when he refused to fight.
The family has leave to seek a conditional pardon to say that he should not have died.
The case was adjourned to allow the family time to gather new evidence.
Edward Fitzgerald QC told the court Pte Farr had a history of treatment for shell shock and had a psychiatric condition.
"Given the evidence of shell shock, the death sentence should not have been carried out and the secretary of state, for that reason, should grant a reprieve," he said.
He said it was now known that on 11 May 1915, Pte Farr "was evacuated to Boulogne with shell shock".
Mr Fitzgerald told the judge: "It is essential to our case that someone who only a year before had undergone five months of treatment for shell shock should not have been executed."
Jonathan Crow, acting for Dr Reid, said he was keeping an open mind and would welcome fresh representations from the family.
Outside the court, Pte Farr's granddaughter, Janet Booth, of Farnham, Surrey, said: "It seems positive. We are hoping things will proceed."
She said earlier that her grandfather's body was probably dumped in a field without a grave.
"They said they weren't fit to have a grave," she added.
Mrs Booth said it was her mother and grandmother who suffered
She said his military pension was stopped and her mother and grandmother were forced out of their house, suffering financial hardship, stigma and shame.
Mrs Booth, 63, said that when her grandfather was executed after being charged and court-martialled, he refused to wear a blindfold.
She said: "He couldn't have been a coward if he stood there open-eyed."
Last year, the then Defence Secretary Geoff Hoon refused to grant a pardon of any kind, but a judge ruled the family had room to argue that Pte Farr had been wrongly refused a conditional pardon.
Mrs Booth, 63, and her husband, Jim, 69, are taking legal action on behalf of Mrs Booth's mother, Gertrude Harris, 91, from Harrow, Middlesex, who was Pte Farr's daughter.