Jeep Repair: 79CJ5 Steering Problem, inch tires, hands on the wheel

Question
I am currently suffering from something I think is called bump steer. I have a 79CJ5 with a 258 straight six with 31 inch tires. When I purchased it, I noticed the steering was a bit erratic but a 79 with no bodyrust couldn't be passed up. The previous owner said it could be adjusted. So when I took it to the shop to have a Weber K551 carb installed, I also asked them to check out the steering. They said I needed a steering shaft, ujoints, etc and a new gear box. I had all those items replaced along with the power steering belt. It does have fluid. An alignment was also done at the same time. No other problems with the front end were mentioned. The problem is when I hit bumps on a road I'm all over the place. The steering is very responsive and I have to keep both hands on the wheel at all times. I previously owned an 81 CJ5 and it didn't have this type of problem. What would you recommend?  

Answer
If your Jeep does not have a steering stabilizer, I would buy and install one. In addition, you might want to look into buying and installing a steering box strenghtening kit.  It's an extra brace between the steering box and the frame.  Make sure your frame is not cracked, that will cause all sorts of problems as well.