"Cogswell" arrived at Pearl Harbor 9 December 1943 for training, and there joined the screen of mighty carrier Task Force 58 for the Marshall Islands operation. At sea on this duty from 16 January to 12 February 1944, when she put into Majuro, "Cogswell" also bombarded Gugewe Island. She continued her screening as the carriers launched raids on Truk on 16–17 February and on bases in the Marianas Islands on 21–22 February, then sailed from Majuro to Espiritu Santo to screen carriers providing air cover for the seizure of Emirau Island from 20–25 March, and raiding the Palaus, Yap, and Woleai from 30 March to 1 April.