"Stormes" remained in port until 27 January 1958 when she embarked on a two-week exercise with other ships of DesDiv 261. The remainder of the year and part of 1959 saw the destroyer taking part in local and fleet operations from New York to the Caribbean. On 7 August 1959, she sailed for her third tour with the 6th Fleet which terminated upon her return to Norfolk on 26 February 1960. The ship entered the Navy Yard on 3 June for a FRAM II conversion which lasted until 5 January 1961. On 24 January, she sailed for Guantanamo Bay where she held refresher training, gunnery practice, and participated in group exercises.