In January 1962, "Robert L. Wilson" participated in recovery operations for a Project Mercury manned space capsule. "Robert L. Wilson" deployed with Task Group Bravo to Northern Europe in February, returning to Norfolk in mid-June 1962. On 1 August 1962 she was again classified DD-847. In September 1962, "Wilson" and the other ships of Destroyer Division 362 deployed to Guantanamo Bay, Cuba as a unit under the command of the Naval Base Commander for the purpose of base defense, and was at Guantanamo and in adjacent waters during the Cuban Missile Crisis in October. "Robert L. Wilson" returned to Norfolk in late November and operated locally until March 1963 when she entered the Philadelphia Navy Yard for a Fleet Rehabilitation and Modernization (FRAM) I modernization. Emerging from her overhaul period in 1964, she continued to serve with the Atlantic Fleet for the balance of that year and throughout 1965.