We present the results of Car-Parrinello (CP) simulations of water at ambient conditions and under pressure, using a rigid molecule approximation. Throughout our calculations, water molecules were maintained at a fixed intramolecular geometry corresponding to the average structure obtained in fully unconstrained simulations. This allows us to use larger time steps than those adopted in ordinary CP simulations of water, and thus to access longer time scales. In the absence of chemical reactions or dissociation effects, these calculations open the way to ab initio simulations of aqueous solutions that require time scales substantially longer than presently feasible (e.g., simulations of hydrophobic solvation). Our results show that structural properties and diffusion coefficients obtained with a rigid model are in better agreement with experiment than those determined with fully flexible simulations. Possible reasons responsible for this improved agreement are discussed. (C) 2004 American Institute of Physics.