The common wisdom that water ice may exist in lunar polar cold traps has become a significant factor in the selection of space research objectives. The purpose of this paper is to address two topics that are missing from the discourse on lunar water: the effect that the pristine cleanliness of the regolith has on water transport on the moon, and the limits on water exposure implied by the extremely high adsorption potentials of the surfaces of soil grains. Water transport is characterized by chemisorption on soil grains and the mixing of wet grains into the regolith by meteoritic gardening. Ballistic lateral flow, which is generally thought to be an efficient conduit for moving water to the poles, is actually a secondary phenomenon that is facilitated by solar wind and micrometeor erosion but not by thermal desorption, as is the case for the dominant lunar exospheric gases, He and 40Ar. Simulation results show that even under the most optimistic conditions, less than 7% of the water accumulated in the regolith resides in the polar cold traps, where water concentrations cannot be greater than 350 ppm. More important, when realistic transport parameters are used in the simulator, the polar water concentration is reduced by almost 2 orders of magnitude. In a word, the concept of water ice at the lunar poles is insupportable.