When simulators are energetically coupled in a co-simulation, residual energies alter the total energy of the full coupled system. This distorts the system dynamics, lowers the quality of the results, and can lead to instability. By using power bonds to realize simulator coupling, the Energy-Conservation-based Co-Simulation method (ECCO) [Sadjina et al. 2016] exploits these concepts to define non-iterative global error estimation and adaptive step size control relying on coupling variable data alone. Following similar argumentation, the Nearly Energy Preserving Coupling Element (NEPCE) [Benedikt et al. 2013] uses corrections to the simulator inputs to approximately ensure energy conservation. Here, we discuss a modification to NEPCE for when direct feed-through is present in one of the coupled simulators. We further demonstrate how accuracy and efficiency in non-iterative co-simulations are substantially enhanced when combining NEPCE with ECCO's adaptive step size controller. A quarter car model with linear and nonlinear damping characteristics serves as a co-simulation benchmark, and we observe reductions of the coupling errors of up to 98% utilizing the concepts discussed here.