Long-range corrected density functional theory (LC-DFT) is applied to a series of small water cluster anions (n = 2-6) to compute their vertical detachment energies (VDEs). The LC scheme is shown to eliminate an unphysical overestimation of the electron-water attraction in the hybrid functional by properly accounting for the long-range exchange repulsions. It is shown that a correct correlation energy behavior for a rapidly varying density is also important for describing a spatially extent, excess electron. The one-parameter progressive (OP) correlation functional, which satisfies this condition, leads to a remarkable improvement in the calculated VDE over the conventional one. The LC-BOP method produces highly accurate VDEs with a mean absolute deviation of 13.8 meV from the reference CCSD(T) results, reducing the error of B3LYP by more than 15 times. LC-BOP is found to be more accurate than MP2 which yields an excess electron underbound by 43.6 meV. The effect of basis sets on the calculated VDE is also examined. The aug-cc-pVDZ basis set with an extra diffuse function is found to be more accurate and reliable than the extended Pople-type basis sets used in the previous works. The extrapolation of the calculated VDE of different electron binding motifs is compared with the VDEs of experimentally observed three isomers (Verlet, J. R. R.; Bragg, A. E.; Kammrath, A.; Cheshnovsky, O.; Neumark, D. M. Science 2005, 307, 93).