Based on these ideas, we proposed a scheme called Adaptive Solvent-Scaling (AdSoS), where the parameter s governing the scaling of the solvent varies as a function of the position of the molecule in space. Starting from an s-value of one in the FG region close to the solute, the value of s is progressively increased across a SG region (buffer layer) to reach a value s max , which is then kept constant in the long-range CG region. By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled number density s 3 ρ for the solvent. Residual density artifacts in and at the surface of the boundary layer can easily be eliminated by means of a grid-based correction potential constructed in a preliminary pure-solvent simulation.