The ship returned to her pattern of cruises to the Mediterranean in 1959, departing Norfolk on 21 September. In 1960, her homeport became Charleston, South Carolina, and in 1961, during her tenth deployment to the 6th Fleet, the ship cruised in the Persian Gulf during the crisis in Kuwait. "Harold J. Ellison" added a new function in January 1962, when she was assigned to Project Mercury as a part of the recovery unit in the Atlantic Ocean. In 1962, she underwent an extensive Fleet Rehabilitation and Modernization (FRAM I) overhaul at the Brooklyn Naval Shipyard. The destroyer rejoined the fleet in early 1963 and through 1964 continued to operate on training and readiness exercises off the Atlantic coast.