i have been avoiding throwing in my 2 cents worth- in fear that some expert bowyer will laugh me off the continent.
if you want to back it- as scars suggests. then thin ca glue, and deer rawhide, going on the back and right around the sides, right up to the belly- have seen that done befor- and it looks kinds cool- doesnt hamper your tillering.
but if you didnt want to back it, thin ca again and wrap it, tiller to a point leaving that area obviously stiffer- but dont go too far, so that you dont hinge it, cut off the wrap, and thin the area to match either side. then re wrap and start all over again- you wouldnt have to cut the wrap everytime you check tiller- but certinally before it gets any where near hinging.
then a nice wrap when you are done!!
i have done this before on a bow , when i didnt have the backing or the knowledge how to back.
it is more tedious but does work.
but if it were me, today- i would do as scars says!
good luck