Luke, I was talking dry heat. See the chapter in TBB 4. Heat treating involves heating the belly until it scorches. There are variations, some like to use a propane torch... just heat the belly fast and turn it black. I prefer to use a heat gun, go slower ( 20-30 min per bow) and heat the wood on the belly to a mild brown that gives off a toasted aroma.
I suggest this first as it's quicker than sinewing. I agree with Marc that sinewing alone ( your original question) will work. Recurving the tips ( use steam or boiling H2O), heat treating the belly and sinewing the back would all be very likely to improve the cast of the bow. Each would raise the draw weight a little, though retillering would be necessary. If you did all three things you'd wind up with an entirely different bow.
Jawge has a point, but I like trying to make a flawed bow better and use it as a learning experience. Maybe once I've built as many as Jawge, I'll be able to except a less than stellar bow and move on to the next.
Ron