She subsequently deployed to the Western Pacific (WestPac) in 1959 and participated in exercises off Borneo and Korea in June and August of that year. Alternating between the west coast and WestPac, "Thomaston" participated in a busy schedule of operations and cruises into the 1960s. During the international tensions brought on by the United States' discovery of Russian missile sites in Cuba, "Thomaston" sailed via the Panama Canal to the Caribbean and operated with the Atlantic Fleet until tensions abated with the withdrawal of the missiles. She then returned to San Diego on 15 December 1962.