I make it a practice to remove all the side buds, leaving one terminal bud per stem. First, to eliminate wasted energy on a bud unlikely to come to full bloom and, secondly, to produce the largest blooms. One of my burgundy-rose peonies has blooms consistently 6 inches in diameter. The white/pinks of last year were also huge. A 6 or 7 year clump has 30 golf ball size or larger buds so I could not see the point of nurturing the small side buds. Does anyone else do this? Some say they leave all buds on to extend the blooming season.
