I cut mine heavy, leaving only a few for myself. All of my peonies, however, have quite long stems that don't require me to take more than one set of leaves. I believe it's the foliage and not the blooms that's required for further flower production. Having said that, my peonies can reach 4' in height and I've pruned them down a bit after blooming. Cutting the flowers or pruning the foliage has never hurt the next year's blooms. The plants continue to expand and grow larger. I have 3 plants of an unknown variety, each in the ground about 10 years, and each has in excess of 100 buds forming.