In 1959, "Quillback" was transferred to Submarine Squadron 12. During 1960, she underwent extensive overhaul at Charleston, South Carolina, to improve her offensive capabilities. She deployed to the Mediterranean in October 1961, returning to Key West in February 1962. Operating locally out of Key West from May to October, "Quillback" was deployed to Guantanamo Bay when the Cuban Quarantine was put into effect and remained there during the first ten days of the Cuban Missile Crisis. During 1963, "Quillback" operated out of Key West and rendered services to the Fleet Training Group at Guantanamo.