"Goodrich" went on alert again with the 6th Fleet during 24 October to 20 November 1962 when the Navy responded to President John F. Kennedy's call for a quarantine of Cuba that choked off the flow of military supplies and enforced the American demands for the withdrawal of the Soviet missile experts and equipment. On 22 July 1966 the destroyer got underway from Mayport on her 13th 6th Fleet deployment. She cruised throughout the Mediterranean for five months, unobtrusively patrolling with the 6th Fleet and taking part in combined naval warfare exercises with units of the Turkish, Greek, British, and Italian Navies. She returned to Mayport on 20 December 1966 for upkeep and type training.