Having elected not to test alongside their main MotoGP rivals at Brno on Monday, Ducati began a private two-day test at Misano on Tuesday.
Valentino Rossi, joined on track by factory test rider Franco Battaini, worked on the chassis updates he had first tried in the test after July's Italian Grand Prix at Mugello.
The changes are intended to concentrate the weight of the Desmosedici. There was no mention of any engine upgrades.
With technical director Filippo Preziosi and team manager Vittoriano Guareschi overseeing the test from the garage, Rossi rode from 10am to 5pm, completing 60 laps.
No lap times were released by Ducati.
Wednesday's final day of testing will be followed by a 15-day break for Ducati before a return to action at the same circuit, for the San Marino Grand Prix, where Rossi's team-mate Nicky Hayden hopes to be fit to return.
Meanwhile, Honda and Yamaha will conduct a two-day test at Aragon on September 4-5.
Rossi is moving back to Yamaha for 2013.