"Shark" put to sea from New York on 26 February and joined Commodore James Biddle's squadron for the suppression of piracy and slave trading in the West Indies. On 25 March, Lt. Perry took formal possession of what is now Key West, Florida, in the name of the United States. He called the island Thompson's Island to honor Secretary of the Navy Smith Thompson and named the harbor Port Rodgers to compliment Commodore John Rodgers. Under orders from Commodore Biddle, "Shark" departed Nassau on 14 August for another cruise to the coast of Africa and returned to Norfolk, Virginia on 12 December 1822. She again sailed for the West Indies in February 1823, and returned to New York on 9 July for repairs. On 5 October, she sailed from New York carrying Commodore John Rodgers and three Navy surgeons to Thompson's Island to determine the fitness of that place as a naval base. She debarked Rodgers and his party at Norfolk on 16 November 1823 before resuming her cruise in the West Indies. She returned to New York on 13 May 1824.