Anionic water clusters have long been studied to infer properties of the bulk hydrated electron. We used photoelectron imaging to characterize a class of (H2O)(n)(-) and (D2O)(n)(-) cluster anions (n less than or equal to 200 molecules) with vertical binding energies that are significantly lower than those previously recorded. The data are consistent with a structure in which the excess electron is bound to the surface of the cluster. This result implies that the excess electron in previously observed water-cluster anions, with higher vertical binding energies, was internally solvated. Thus, the properties of those clusters could be extrapolated to those of the bulk hydrated electron.