We consider suffix tree construction for situations with missing suffix links. Two examples of such situations are suffix trees for parameterized strings and suffix trees for 2D arrays. These trees also have the property that the node degrees may be large. We add a new back-propagation component to McCreight's algorithm and also give a high probability perfect hashing scheme to cope with large degrees. We show that these two features enable construction of suffix trees for general situations with missing suffix links in O(n) time, with high probability. This gives the first randomized linear time algorithm for constructing suffix trees for parameterized strings.