We report here the correlation between the water content and superconductivity in Na0.3CoO2*yH2O under the influences of elevated temperature and cold compression. The x-ray diffraction of the sample annealed at elevated temperatures indicates that intergrowths exist in the compound at equilibrium when 0.6 < y < 1.4. Its low-temperature diamagnetization varies linearly with y, but is insensitive to the intergrowth, indicative of quasi-2D superconductivity. The Tc-onset, especially, shifts only slightly with y. Our data from cold compressed samples, on the other hand, show that the water-loss non-proportionally suppresses the diamagnetization, which is suggestive of weak links.