On 4 September, "Thompson" departed San Francisco for a shakedown training cruise which took her as far southward as Magdalena Bay in Baja California Sur. She returned to San Diego, on 29 September, to operate with the Battle Fleet as part of Destroyer Division (DesDiv) 32, Destroyer Squadron (DesRon) 11. After initial fleet operations off the west coast, "Thompson" departed from San Diego on 7 January 1921, to take part in fleet maneuvers off Panama and later off the Chilean coast, south of Valparaíso.