We study the fundamental efficiency of delimited control. Specifically, we show that effect handlers enable an asymptotic improvement in runtime complexity for a certain class of functions. We consider the generic count problem using a pure PCF-like base language λ_b and its extension with effect handlers λ_h. We show that λ_h admits an asymptotically more efficient implementation of generic count than any λ_b implementation. We also show that this efficiency gap remains when λ_b is extended with mutable state. To our knowledge this result is the first of its kind for control operators.