Anionic water dusters are generally considered to be extremely challenging to model using fragmentation approaches due to the diffuse nature of the excess electron distribution. The local correlation coupled cluster (CC) framework cluster-in-molecule (CIM) approach combined with the completely renormalized CR-CC(2,3) method [abbreviated CIM/CR-CC(2,3)] is shown to be a viable alternative for computing the vertical electron binding energies (VEBE). CIM/CR-CC(2,3) with the threshold parameter zeta set to 0.001, as a trade-off between accuracy and computational cost, demonstrates the reliability of predicting the VEBE, with an average percentage error of similar to 15% compared to the full ab initio calculation at the same level of theory. The errors are predominantly from the electron correlation energy. The CIM/CR-CC(2,3) approach provides the ease of a black-box type calculation with few threshold parameters to manipulate. The cluster sizes that can be studied by high-level ab initio methods are significantly increased in comparison with full CC calculations. Therefore, the VEBE computed by the CIM/CR-CC(2,3) method can be used as benchmarks for testing model potential approaches in small-to-intermediate-sized water clusters.