The most effective thing you can do is pull comps from HCAD or other sources for similar SF in your area that are lower than their assessment of your house. You can get pretty creative if you put your mind to it and augment the lower comps you find. Tell them your roof leaks since the hurricane. Tell them the house next door is a rental unit and the cops are always there, therefore depreciating the value of your home. I told them the manhole cover in front of my home always emits a fowl odor and the city won't do anything about it. They're not going to come out and sniff the manhole cover so how would they know if you're fudging a bit. I've always had mine reduced each year. Sometimes more than others, but I always got something.
Thank you for those suggestions, Prolix R. I actually have some very legitimate reasons then. Because, for me, the increases have been relatively small I have not been proactive. This year was the first year I really considered it.