A novel combination of minima-hopping with translational and topology-modifying steps is used to locate putative global minima for TIP4P water clusters, (H2O)(n). Our minima for n <= 30 agree with previous results in all but two cases (n = 28; 29) for which we report lower-energy structures. New candidates are reported for the global minima of clusters with 31 <= n <= 37. A clathrate-like structure with one water molecule in a cage first appears as the global minimum for n = 19 but the motif becomes persistent only for n > 24. Global minimum structures with two internal molecules appear first for n = 26 and then for n > 30. (c) 2009 Elsevier B.V. All rights reserved.