We study the problem of efficiently charging a set of rechargeable nodes using a set of wireless chargers, under safety constraints on the electromagnetic radiation incurred. In particular, we define a new charging model that greatly differs from existing models in that it takes into account real technology restrictions of the chargers and nodes of the network, mainly regarding energy limitations. Our model also introduces non-linear constraints (in the time domain), that radically change the nature of the computational problems we consider. In this charging model, we present and study the Low Radiation Efficient Charging Problem (LREC), in which we wish to optimize the amount of "useful" energy transferred from chargers to nodes (under constraints on the maximum level of imposed radiation). We present several fundamental properties of this problem and provide indications of its hardness. Finally, we propose an iterative local improvement heuristic for LREC, which runs in polynomial time and we evaluate its performance via simulation. Our algorithm decouples the computation of the objective function from the computation of the maximum radiation and also does not depend on the exact formula used for the computation of the electromagnetic radiation in each point of the network, achieving good trade-offs between charging efficiency and radiation control; it also exhibits good energy balance properties. We provide extensive simulation results supporting our claims and theoretical results.