One of the most promising techniques to drastically reduce the energy consumption of cellular networks is the use of sleep-mode (SM) methods: when the traffic load is low, some components of the network, such as a base station (BS), can be switched off. In this case, the traffic load is managed by BSs that stay on. In this paper, we investigate how user cooperation can further reduce the energy consumption of a cellular network that uses SM strategies. In particular, we study how sleeping periods can be extended when users tolerate a delay before the start of their service. We propose two delay-tolerant-user-aware SM strategies and provide mathematical grounds for the evaluation of their performance. We evaluate the strategies in the context of LTE networks with realistic daily traffic patterns. The results show considerable daily energy reductions (up to 21% compared to the always- on paradigm and up to 15% compared to the SM strategy without user cooperation)