Watch cerrone vs cote; trail hand overhand is one of the best tools in the cage, but in certain situations it is also very easy to counter. Like many things in mma, it all revolves around the takedown threat.
Someone worried about you shooting in will often be cautious about moving forward, and may be looking to poke with a jab or side kick. The overhand accomplishes several things here; it can be thrown with the same movement for closing the distance, it takes your head off the centerline, and either crosses your opponents strike, or loops around his hands and splits his guard if he shells up. It is very reliable in this situation and there is a reason so many different fighters have so much success with it.
The way you can deal with it is in many ways isomorphic with the above; the number one way to punish someone moving into you is with the counter double, and the overhand even more so. With the level change you avoid the strike completely, the opponent is planted and strait up, and you are both moving together allowing you to get deep on the hips and under his center of gravity. The takedown practically takes care of itself.
Even someone with only average TDs and plant someone with much better TDD in that situation. Cerrone is hardly known for his wrestling, but every time Cote looked to throw his overhand, Cerrone hit the reaction shot and put him on the ground. After doing this two or three times, Cote stopped throwing the overhand, and without the threat of this vital tool, he was picked apart in neutral.
