I really don't see where an over/under grip would necessarily increase the chance of a torn bicep unless your arms are bent when pulling and you yank the bar off the floor. I've officially deadlifted 600 lbs with an over/under grip and have used this grip style for years and have never had any issues with biceps pulls.
That being said, I haven't used an over/under grip since my powerlifting days and it doesn't do much to aid in achieving a balanced grip. I would work on grip strength exercises that improve your grasping power. Just for fun you could have your hand strength verified with a Hand Dynamometer to compare which hand is the weaker of the two.
As mentioned earlier a weightlifting hook grip will help as well as chalking your hands up with a quality gym chalk. Lifting on a bar with proper knurling will also aid in securing a good grip.
Originally Posted by Andrew Durham
Yesterday I was at the local gym doing my OHS with my usual crew. Next to the squat rack is a platform. One of the trainers had his client doing deadlifts. She was dropping the weight, saying that she is unable to hold on without it slipping. My friend suggested that she do mix grip. He, the trainer, said that he doesn't allow his clients to do mixed grip deadlifts. He said that over time it will cause elbow problem. Has anyone else heard this? Googled it and didn't see anything of the sort.