Lieutenant John Gibson commissioned "Speedwell" in July 1780, for the Mediterranean. She arrived at Gibraltar, which was undergoing the Great Siege, on 20 December, carrying dispatches. While "Speedwell" was on her way she encountered a small vessel that launched an attack that "Speedwell" repulsed, though Gibson sustained some wounds. On 1 January 1781 the British took possession of an abandoned settee on which there were letters, with one mentioning that the vessel that had attacked "Speedwell" had suffered several men killed and wounded.