From the Botany Photo of the Day comments on Paeonia rockii: (note -- this is in relation to the kinds of peonies one would plant in the backyards of Pennsylvania, not Paeonia rockii)
The dead head comment is generally true. I think it redirects the plants energy to more productive areas, like root development. Had not heard about the fertilizer idea before. I read an article once that said bone meal was suppose to be good. I work that into the ground before blooms, after blooms and in the fall.