Eddie Paradise grew up in the same neighborhood as his friend and fellow soldato, Cosimo Barone. He was 'made' after Nick Geraci took over the regime of Salvatore Tessio. He was recognized as a tough enforcer for the family.
Paradise got his nickname, 'The Turtle', as he was a very slow man in his life physically. Eddie and Nick Geraci were also very good friends and got along well. After Geraci's disposal in 1962, Eddie became the junior caporegime in the family and took over the "Tessio Regime" in Brooklyn. He was chosen over 'Momo' Barone, an event that came back to hunt Michael Corleone.
He was never put in charge in the effort to locate Geraci, instead to keep an eye on Barone. In 1963, he was put in charge of a commission meeting on his territory, the BQE expressway. After the police came to take away Tom Hagen, everybody blamed Paradise for the misfortune. He was known to have many misfortunes happen to him.
In 1964, Geraci was lured to a meeting that he thought would make him the boss of the Corleone family. It was an ambush, as Eddie was forced to kill Geraci, and a cowardly Momo Barone, who had been unable to kill Geraci himself. Paradise got his reputation back after this and was respected by the family again.
The surname 'Paradise' is derived from the Italian surname 'Paradiso', which may have been Paradise's original surname.