To support simplifying assumptions used in analytic theories of aqueous systems, we have used computer simulations to examine correlations in the bonding of the individual sites of a water molecule using two qualitatively different extended primitive models, EPM4 and EPM5. We have studied these correlations not only for the fully interacting water molecule (considered as a solute) but also for a series of other solutes made from the water molecule by turning off some of its interaction sites. We have found that for the EPM5 solvent the local density of water molecules bound to a specific site is independent of the state of the other sites being turned on or off; for the EPM4 solvent such an independence does not hold exactly, but the correlations have been found to be very small. These facts fully justify previously used speculative approximations for the calculation of the solvation Helmholtz free energy of a water molecule, and also lend support to the first-order thermodynamic perturbation theory of Wertheim. (C) 2003 American Institute of Physics.