On 8 May 1969, "Alacrity" put to sea, once more bound for the Mediterranean. After five months with the U.S. 6th Fleet engaged in training exercises and port visits, the minesweeper headed back to the United States on 11 October. She reached Charleston on 30 October. Then, except for 12 days underway for special operations at the beginning of December, the warship spent the remainder of the year in port at Charleston  In 1970, "Alacrity" conducted exercises out of her home port until mid-June. On the 17th of that month, she entered Avondale Shipyards, Inc., for a regular overhaul. The minesweeper completed repairs and left New Orleans, Louisiana, on 1 December. She returned to Charleston on the 6th and, after holiday leave and upkeep, resumed normal operations. After seven months of exercises, drills, and inspections out of Charleston, "Alacrity" headed back toward the Mediterranean on 2 August. She entered the "Middle Sea" late in August and spent September and the first week in October steaming in the western Mediterranean and making port visits. "Alacrity" returned to Rota, Spain, on 7 October and two days later sailed for the United States. She returned to Charleston on 27 October and, except for a week at sea for special operations in the middle of December, spent the remainder of the year in her home port. On 10 January 1972, "Alacrity" departed Charleston for an eight-day, cold weather, amphibious exercise off the shores of Maine. By the end of January, the minesweeper was back in Charleston and, in February, resumed normal operations. In April, she interrupted her schedule to provide support for the Apollo 16 moon shot. She resumed operations out of Charleston late in April and remained so occupied almost until the end of the year. Early in December, she returned to the vicinity of Port Canaveral, Florida, to assist in gathering data during the Apollo 17 moon shot. "Alacrity" concluded that duty at Charleston on 8 December and remained in port for the rest of 1972. The warship spent the first four months of 1973 working out of Charleston. On 10 May, she entered Detyen's Shipyard in Mount Pleasant, South Carolina, for modifications. On 1 June 1973, "Alacrity" was redesignated "AG-520". She left Detyen's Shipyard on 23 July and returned to the Naval Station, Charleston, where she remained until 5 August.