In the 1960s "Robert A. Owens" continued to rotate between 2nd and 6th Fleets. In November 1960 and February 1962, she assisted in the recovery operations for Project Mercury space capsules, Mercury 2 and Mercury 6. After the latter, "Robert A. Owens" sailed east to join Task Group Bravo (TG Bravo) for eastern Atlantic antisubmarine operations. Reclassified DD-827 on 7 August 1962, she was a unit of the Cuban Quarantine Task Force 136 during October and November. In January and February 1963, she conducted anti-submarine warfare (ASW) operations in the Atlantic. March brought another period of patrol off Cuba; and, in April, "Robert A. Owens" again got underway for extended deployment. Duty in the Mediterranean, the Red Sea, and the Indian Ocean followed and on 23 December she entered the Norfolk Naval Shipyard for Fleet Rehabilitation and Modernization (FRAM) overhaul.