We have a lilac about twenty feet high with numerous new growth branches sprouting up in the middle of the older growth. They appear to do nothing but consume sap as there were no flowers on them last year and the tree as an whole did not flower much. I would like to improve the health of theis tree and promote more flowers but have not been able to find much guidance yet. Can anyone help? Should I cut all of the non flowering branches from the middle of the tree as well as cut back some of the older branches? Any suggestions would be appreciated.