Multiple subcarrier modulation is an appealing scheme for high-data rate optical communication. However a major drawback is its low average power efficiency. While subcarrier reservation is a common approach to combat this problem, little is known about the performance of algorithms that utilize subcarrier reservation. By combining properties of sparse signals with an abstract form of the Uncertainty Principle related to multiple subcarrier signals, we design an effective iterative method for constructing average-power-efficient multicarrier signals. Unlike most existing subcarrier reservation methods, our method provides a guaranteed bound for the achievable average power reduction as well as guaranteed rates of convergence. Numerical simulations demonstrate the performance of the proposed method.