Traditionally cellular networks have been dimensioned for providing seamless coverage and meeting the user demand with little regard to their energy consumption. Recently, the focus has been moved to seeking ways to increase the energy efficiency by better adapting to the existing users behaviors. In this paper, we are going a step further in studying a new type of disruptive service by trying to answer the question "What are the potential energy efficiency gains if some of the users are willing to tolerate delays?". We present an analytical model of the energy usage of LTE base stations, which provides lower bounds of the possible energy gains under a decentralized, non-cooperative setup. The model is analyzed in six different scenarios (such as micro-macro cell interaction and coverage redundancy) for varying traffic and user-tolerable delays. We show that it is possible to reduce the power consumption by up to 30%.