Placing the bars only 2cm below the saddle would be a recreational fit, intended for comfort. Racers nearly always use a much larger saddle to bar drop to improve aerodynamics. One of the keys to using a large 9-11cm (around 4 inch) saddle to bar drop is having the saddle back far enough to balance your weight over the saddle, so there is little weight on your hands. Fitters who use the old knee-over-pedal method of positioning the saddle, will often have it too far forward for comfort, using a large saddle to bar drop.

Changes to the saddle to bar drop should be made slowly, so you have time to get used to the change.

Several years ago, I made a change from a 9cm drop to 11cm all at once and it worked out fine, but that's probably because I had been using such a large drop for many years prior to the change.