E-health applications have emerged as a promising approach to provide unobtrusive and customizable support to elderly and frail people based on their situation and circumstances. However, due to limited resources available in such systems and data privacy concerns, security issues constitute a major obstacle to their safe deployment. To secure e-health communications, key management protocols play a vital role in the security process. Nevertheless, current e-health systems are unable to run existing standardized key management protocols due to their limited energy power and computational capabilities. In this paper, we introduce two solutions to tailor MIKEY-Ticket protocol to constrained environments. Firstly, we propose a new header compression scheme to reduce the size of MIKEY's header from 12 Bytes to 3 Bytes in the best compression case. Secondly, we present a new exchange mode to reduce the number of exchanged messages from six to four. We have used a formal validation method to evaluate and validate the security properties of our new tailored MIKEY-Ticket protocol. In addition, we have evaluated both communication and computational costs to demonstrate the energy gain. The results show a decrease in MIKEY-Ticket overhead and a considerable energy gain without compromising its security properties.