Comanchero outlaw bikie gang leader Vincenzo Focarelli remains in hospital under police watch after an attack that claimed his son's life.

Vincenzo Focarelli suffered four gunshot wounds in the fourth attempt on his life on Sunday, but his son Giovanni Focarelli, 22, died after both men were shot in Adelaide.

His lawyer Stacey Carter has told The Advertiser newspaper that Focarelli would be undergoing more surgery to remove a bullet fragment from his head.

He is at Royal Adelaide Hospital under police guard. But police expect he will refuse protection when he leaves.

Focarelli has refused to help police find the murderer of his son.

It's not the first time he has refused to cooperate with police, despite being shot in December and being the target of a failed bomb attack.

Focarelli tried to drive Giovanni to hospital after the shooting but his son was dead by the time he flagged down a police car for help.

Tributes to Giovanni were posted on the New Boyz Support Crew Facebook site on Tuesday, including one that described him as a top bloke: "The man was down to earth, kind and wasn't afraid of going up to any woman to have a go."

"I'm going to miss him and I think he deserved better.

"Gio, you were a true man, good friend and top bloke."

Attorney-General John Rau has insisted crime rates are falling and the state has the lowest reoffending rate in the nation, at 19.1 per cent of offenders, according to a report from the Productivity Commission.

"The South Australian government's effort to reduce crime is working well," Mr Rau said.DISCLAIMER:Text may be subject to copyright.This blog does not claim copyright to any such text. Copyright remains with the original copyright holder.