FLAT SIDED NO GIRTH GROOVE
Much of that written about the Herring Gutted Horse applies here.
There is no natural girth groove and as such it is difficult to anchor the girth sufficiently without relying on a breastplate or hunting martingale and as an extra security measure this is essential. The saddle will be inclined backwards and any design which prevents the shoulder from destabilising the saddle is recommended.
The problem will be more acute the further forward cut the flap and panel are and less obvious in straight cut and dressage saddles. Changing the position of the girth straps is often useful.
A significant advance in this is the saddle with the floating point as described under Herring Gutted