QuestionsHow to growFlowersBorder Perennial FlowersDead heading 0 Vote Up Vote Down Carol Davis asked 14 years ago Which flowers should and should not be dead headed? 1 Answers 0 Vote Up Vote Down Gerry Daly Staff answered 6 years ago No flower must be dead-headed, but almost any can … if you have the time and the inclination. Dead-heading can extend the flowering period for sweet peas, petunias and roses.