When making chairs of this ilk, I like to glue the entire backs together as separate assemblies. I then repeat the process with the front legs/seat rails and finally take the side seat rails and remaining stretchers and glue the whole lot together.
I dry-assemble the stiles, back seat rails and backsplats in order to establish the shoulders for the tenons on the tops of the stiles and splats. That done, I form the tenons and cut the mortises in the crest rails to match (figure 1).
Each component is shaped and rough-sanded except where they intersect with another. As can be seen by the pencil marks (click the above image to enlarge it), the junctures are left oversized until glued and assembled whereupon all are faired.
As with these two chairs, it is common for Irish chairs’ splats to be tenoned directly into the back seat rails (as opposed to into fixed shoes) and the shoes – more like ‘slippers’ – simply slip into position against the fronts of the splats (figs. 2 & 3).
Each shoe is retained with a couple of headless brads.