Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site molecular fluids has so far been limited by complications due to the implicit molecular geometry constraints on the site densities, whose resolution typically requires expensive Monte Carlo methods. Here, we present a general scheme of circumventing this so-called inversion problem: compressed representations of the orientation density. This approach allows us to combine the superior iterative convergence properties of multipole representations of the fluid configuration with the improved accuracy of site-density functionals. Armed with the above general framework, we construct a simplified free-energy functional for water which captures the radial distributions, cavitation energies, and the linear and nonlinear dielectric response of liquid water. The resulting approach will enable efficient and reliable first-principles studies of atomic-scale processes in contact with solution or other liquid environments. © 2013 Elsevier B.V. All rights reserved.