We investigate insertion and deletion models for hierarchical phrase-based statistical machine translation. Insertion and deletion models are designed as a means to avoid the omission of content words in the hypotheses. In our case, they are implemented as phrase-level feature functions which count the number of inserted or deleted words. An English word is considered inserted or deleted based on lexical probabilities with the words on the foreign language side of the phrase. We propose novel thresholding methods in this work and study insertion and deletion features which are based on two different types of lexicon models. We give an extensive experimental evaluation of all these variants on the NIST Chinese-English translation task.