Reasons for denial

I was just told that they will deny you for careless driving tickets and a few other soeeding violations. I had 2 when I was 18-20 and before I spend the money on this process I was curious of this is true and if it was/was not what are some things I should worry about. Ive never gotten into any real trouble other then 2 careless driving tickets and 3 speeding tickets. My record has been perfect for over 13 years now.