Miriam,
Are you using a variable speed drill (hopefully yes)? If so you really just need more practice.
Suggestions would be to stop short of setting the screw and use a screwdriver (I often do this on sensitive joints). And I normally hand-tighten after using the drill on important joints as well (get a much better torque feel with your hand vs. the drill).
Another suggestion would be to pre-drill (and countersink) before driving the screws (use one of the combo drill/countersink bits). This would give you a better overall result as well (and makes it easier to stop at the correct depth/place). I did all my 1/4 attachment this way (in fact nearly all screws in my tear are countersunk) as luan is very touchy when trying to power set a screw.