You will learn that the Secretary of State doesn't reinstate convicted drunk drivers who continue to drink six beers in one sitting. I recommend that you reduce your alcohol usage and try after a year of responsible drinking.
Not many people get convicted of Dui with a .10 BAC and no priors. The fact you did not receive supervision may be that you got the DUI in Champaign and are under 21, you had an accident or you represented yourself. Your cooperation with the system will not impress the SOS at all. Your cooperation may have caused you to plead guilty thinking it would help you.
There is one fact you provided here that leaves me with little doubt that you will be denied. The denial letter will tell you why and that you can have another hearing every 30 days. Good luck. I am afraid you will need it.
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