The structure of water and the energy of its interaction with a fragment of B-DNA composed of 12 based-pairs and with the corresponding sugar and phosphate units and Na+ ions (at each phosphate group) are analyzed using Monte Carlo stimulations. The sample of water molecules, at the stimulated temperature of 300 degrees K, is composed of 447 water molecules. The results are discussed either in terms of a statistical analysis over the two million stimulated conformations (after equilibration) or with reference to an "average configuration." A comparison is made with a simulation previously presented for the same system but without counterions. Isotherms at different relative humidity, hydration, and tentative reactivity scales for different sites; the hydration number at each site; and the structure of interphosphate and intraphosphate hydrogen bonded filaments of water are reported and discussed. The stabilization of the B-conformation induced by the solvent with counterion ("ion-induced compression effect") is analyzed on the basis of the above findings. The analysis presented is very detailed to allow refined interpretations of spectroscopic (infrared, Rahman, and nmr) and scattering (x-rays and neutron beams) data on DNA in solution.