anti-submarine warfare tactics with units of the British Fleet, and cleared that port 25 November to resume her training duties at Key West, 11 December. She again sailed from Key West 6 January 1958 and arrived at Gibraltar 18 January. Her tour with the Sixth Fleet included participation in operation "ASCENDEX" and visits to the ports of Palma and Barcelona, Spain; Port de Monaco; and Genoa, Italy. She sailed from Gibraltar on 18 August and conducted hunter-killer exercises with destroyers in waters off Cuba and Jamaica before returning to Key West 11 October.Picuda underwent overhaul in the Charleston Naval Shipyard from 13 October 1958 to 12 March 1959, followed by a brief period of refresher training in the New London, Connecticut–Newport, Rhode Island, area. She resumed her former duties at Key West on 27 March 1959 and put to sea from that port 1 June for her third Mediterranean tour. She touched at Norfolk 4 June and reached Gibraltar on 15 June. Operations in the Mediterranean during this tour included visits to Naples and Genoa, Italy; Marseilles, France; and Lisbon, Portugal. She departed the latter port 26 August to resume training duties at Key West, Florida.Picuda was brought to Pensacola, Florida during the 50th Anniversary of Naval Aviation and people were allowed to board her to see inside. In 1961, Picuda visited Guantanamo Bay and underwent a five-month overhaul at Charleston Naval Shipyard. During 1962, Picuda visited Guantanamo Bay twice before making a circumnavigation of the South American continent, conducting joint operations with Brazil, Argentina, Uruguay, Chile and Peru. This operation was terminated due to the Cuban Missile Crisis, and Picuda proceeded to Key West, Florida. Picuda spent most of 1963 operating out of her homeport of Key West making one trip to Guantanamo Bay. During 1964, Picuda operated out of Key West in the Atlantic and Caribbean, winding up the year with an overhaul in the Philadelphia Naval Shipyard. Picuda made another visit to Guantanamo Bay in 1965. She began 1966 with a three-month Mediterranean tour with the Sixth Fleet, participating in fleet ASW exercises and NATO exercises with French and Italian naval forces. She wound up the year with another visit to Guantanamo Bay. During the 1967 North Atlantic NATO operation "Quick Pursuit," Picuda lost two men at sea (Lieutenant (junior grade) Jerry R. Alexander and Chief Torpedomans Mate Robert E. Small). She visited Bergen, Norway and Portsmouth,