ETSI Multi-access Edge computing (MEC) main purpose is to improve latency and bandwidth consumption by keeping local traffic local while providing computing resources near the end-user. Despite its clear benefits, the next-generation of hyper-distributed applications (e.g., edge robotics, augmented environments, or smart agriculture) will exacerbate latency and bandwidth requirements, posing significant challenges to today's MEC deployments. In this work, we leverage on the current study item ETSI GR MEC 036, introducing a lightweight constrained version of a MEC platform that can be deployed in a mobile end terminal or in its closed locality. This work presents design options for cMEC, and how it can untangle the aforementioned gaps while being architectural compatible with a full-fledged MEC framework. Finally, key use cases and still open challenges are discussed, including recommendations to extend the current MEC standard towards constrained environments.