I am practicing dovetails and so I have made various stools of differing sizes consisting of three pieces of rectangular wood: one for the seat and two for the legs, being joined with dovetails.
I want to put a joining piece between the two legs to prevent splaying under heavy load.
I can't find much information on what the proper joint for this would be. I would rather not go all the way through the legs for something like a pull-through dovetail just because I haven't done it before and don't want to ruin the stool (which is for my dad).
I was thinking of just a simple T-butt joint but I have been reading that it is very poor for a joint which needs to take any tension. Does adding some small dado to the accepting end of the butt-joint help increase the tensile strength of the joint in any substantial way?
In terms of my tools... pretty sparse. I have chisels, hammer, and a dovetail saw; along with copious amounts of sand paper :P
Since I have gotten this far without any metal I am also going to avoid any mechanical fasteners.
Edit:
I added a rough picture showing the current three parts and where I want to put the additional piece (green). Thanks.

