"Norris" next served in Task Force Bravo, an experimental anti-submarine development group, until her next 6th Fleet duty from June–August 1960. After a FRAM II conversion at Philadelphia from March to December 1961, "Norris" had over a year of intensive Atlantic Fleet training operations, including a midshipman training cruise. She was reclassified a general purpose destroyer (DD-859) on 7 August 1962 and in October took station off Cuba during the quarantine provoked by the missile crisis. With the return of quiet, she was back in Newport in December to prepare for another Mediterranean deployment, which took place from 6 February–7 July 1963. In August, an experimental wire-guided torpedo system was installed by Boston Naval Shipyard, and "Norris" spent much of the next year testing and evaluating the new system.