In this paper, the green operation of heterogeneous LTE cellular networks is investigated. In addition to macrocells, small cells are used to offload traffic and increase the capacity of the network. A combination of mains-powered small cells and renewable energy small cells (RESCs) is considered, where the latter corresponds to small-cell base stations powered by renewable energy sources, e.g., solar panels or wind turbines. Thus, the presence of RESCs allows not only to offload macrocell traffic but also to optimize energy performance by switching off other mains-powered small cells whenever possible. Both the uplink and downlink directions are considered in the analysis, while taking into account dynamic resource allocation and the impact of intercell interference. A utility maximization approach is proposed, where weighted utility functions take into account both the quality-of-service (QoS) performance of the network and its energy consumption. The use of RESCs for utility enhancement (RESCUE) leads to interesting results, especially when the utility function presents a judicious balance between QoS and energy efficiency.