A brutally efficent Director of the CIA, Soffet was disconcerted when James Shea came to power, largely due to Shea's favour of his brother Danny, who he later gave the title of Attorney general. In the late 1950s, Soffet had his people arrange a hit on Fidel Castro, the President of Cuba, by using his connections with Michael Corleone, Louie Russo and Carlo Tramonti.
In 1961, President Shea had Soffet assemble a crack team of assassins designated to kill Castro. However, another assassin, Carmine Marino, managed to hit Castro's double, and was later arrested and murdered by CIA Agent Joe Lucadello, to prevent him from causing any controversy.
It is unknown as to whether Soffet ordered this hit or not.