Opposite to the original cloudlet approach in which an edge is utilized to bring the cloud and its benefits closer to the applications, in cloud- and edge-connected IoT systems where the applications are deployed and run in the cloud, we exploit the edge somewhat differently, either by bringing the physical world and its data up closer to the cloud or by caching parts of the applications down closer to the physical world. Aggressive optimizations seeking substantial IoT energy savings are needed to maintain the scalability of large-scale IoT deployments and to stay within cloud cost constraints (avoiding costly elasticity when working with a budget limit). In this paper, we present a novel optimization approach that relies on the simple principle of minimizing all movements: movements of data from the IoT up to the Edge and Cloud, and movements of application fragments from the cloud down to the edge and the IoT itself. Our approach is novel in that it involves and utilizes the dynamic characteristics and variability of both the data and applications simultaneously. Another novelty of our approach is the definition and use of "sentience-efficiency" as a precursor to "energy-efficiency" for achieving truly aggressive savings in energy. We present our bi-directional optimization approach and its implementation in terms of algorithms within an architecture we name the cloud-edge-beneath architecture (CEB). We present a performance evaluation study to measure the impact of our optimization approach on energy saving.