half pads usually do more harm than good with an I'll fitting saddle. If the saddle fits well or is slightly to narrow the half pad will make it a tighter fit and usually pinches them when riding.
I use a square pad (prefer a bit thicker ones to really flimsy ones...too many washings and they just don't have enough left in them for my purposes) with a Tad Coffin leather half pad, the thinnest option. My saddle is slightly too wide for my horse and the leather half pad makes it fit perfectly.
When I show, I use a Toklat Medallion SuperQuilt shaped pad or the same in a half pad (with the foam pieces removed). These pads are as thick as my schooling set-up by themselves, so it's all I use.
Right now, I use my saddle on one other horse and he gets just a poly pad.