As you corner, the tread deforms and in the case of the front tires,
causes the car to steer on a different line than you are pointing it.
To inexperienced people, you get the feeling that the car is sliding
or drifting off line. It is actually the tires changing your direction.
To eliminate this, you reduce the tread height to a level where it tends
not to roll over. Big chunky tread designs shaved to 3/32 of an inch
is what most people use. I have no idea what kind of competion you
are planning but in most, they inspect the tread depth and will
disqualify you if it is too shallow. Another caution is that there are
cheaters in every level of competion and some one will always find
a set of tires that have been recapped with butyl that provides about
6X street rubber traction.

(if you want to know the name of the guy in Norfolk, VA, that does
the butyl recapping, don't contact me)