This paper investigates several joint power allocation and relay selection strategies for wireless cooperative networks with Amplify-and-Forward(AF) protocols. These strategies aim at minimizing the total power consumption subject to some given Quality of Service(QoS),which can be formulated to convex optimization problems. Using standard convex optimization techniques,closed-form solutions to these problems are obtained. Simulation results show that the proposed strategies can achieve lower power consumption than the traditional random relay selection and equal power allocation strategy.