Advances in computing hardware and novel multimedia applications have urged the development of handheld mobile devices such as smartphones and PDAs. Video content is increasingly consumed daily in mobile devices as well as in first response emergency services. With this significant increase of cloud-based video delivery, one of the challenges is how to efficiently transmit the bulky videos to resource-constrained mobile devices. Despite the attractive features of the widely-used approaches on the bitrate adaptation such as DASH standard, video delivery impose significant demands on the limited battery capacity of mobile devices. Thus the development of efficient approaches to decrease the amount of streamed data while maintaining maximum possible quality with the aim of increasing the battery lifetime has become a key research topic. In this pilot work, we run an offline study towards energy-aware delivery of cloud video segments to mobile devices with limited energy budget over wireless networks, with the aim of integrating into DASH standard. Our results show that our proposed adaptation significantly improves the quality of information per unit of energy consumed to deliver videos to mobile devices.