In this work we investigate the electrostatics of fully-depleted cylindrical nanowire (CNW) MOSFETs accounting for quantum effects and, in doing so, we propose a new approach for the self-consistent solution of the Schroedinger-Poisson equations based on a rigorous time-independent perturbation approach. The strength of this method is that the Schroedinger equation is solved in a semi-analytical form, thus eliminating discretization errors and providing very accurate energy eigenvalues and eigenfunctions; furthermore, the computation time is cut down by an order of magnitude. A major result of this investigation is that the ON/OFF current ratio increases as the diameter of the CNW-MOSFET is scaled down. This makes them good candidates for an advanced low-leakage CMOS technology. The above technique is finally used to investigate the influence of high-k gate dielectrics on the electrostatics of CNW-MOSFETs, indicating that an improved performance is achieved, though not as large as one would expect from the k ratio.