We employed a four-step searching/screening approach to determine best candidates for the global minima of (H2O)11 and (H2O)13. This approach can be useful when there exist a large number of low-lying and near-isoenergetic isomers, many of which have the same oxygen-skeleton structure. On the two new candidates for the global minimum of (H2O)11, one isomer can be viewed as placing the 11th molecule onto the side of the global minimum of (H2O)10 and the other can be viewed as removing the 12th molecule from the middle layer of the global minimum of (H2O)12. The three leading lowest-energy clusters of (H2O)13 can all be built starting from the global minimum of (H2O)12, with the difference being in the location of the 13th water molecule.