Fixing Slop of Gear on Hex Shaft

[kitare102]

Our shooting mechanism rotates up and down on a hex shaft driven by a hex gear on the shaft. Picture here: http://imgur.com/S4qvkzd. While having a good amount of slop between shaft and gear is alright for gearboxes, it makes our design difficult, as the arm can rotate by a few degrees without moving the gear. This presents a problem when using a PID loop to control the angle, as getting to the position quickly or driving while maintaining the angle causes the arm to bounce up and down fairly rapidly. We've tuned the PID loop such that the effect isn't terrible, the there are still ranges in the motion of the arm that bounce a lot. Does anyone have an idea as to what we could do to the gear or the shaft that would (robustly) remove the slop between the two? Tell me if any more specific information would help.