The responsible use of water, as well as its reuse and purification, has been a major problem for decades now. In this work, we study a method for adsorbing ions from aqueous solutions on charged interfaces using highly porous electrodes. This water purification process is based on the electric double layer concept, using the method known as capacitive deionization (CDI): If we pump salty solutions through the volume comprised between two porous electrodes while applying a potential difference to them, ions present in the solution are partially removed and trapped on the electrode surfaces. It has been well established that the use of carbon electrodes in combination with ion exchange membranes (membrane-CDI) improves the efficiency of the method above that achieved with bare activated carbon. Another approach that has been tested is based on coating the carbon with polyelectrolyte layers, converting them into "soft electrodes" (SEs). Here we investigate the improvement found when combining SEs with membranes, and it is shown that the amount of ions adsorbed and the ratio between ions removed and electrons transported reach superior values, also associated with a faster kinetics of the process. The method is applied to the partial desalination of up to 100 mM NaCl solutions, something hardly achievable with bare or membrane-covered electrodes. A theoretical model is presented for the ion transport in the presence of both the membrane and the polyelectrolyte coating.