Parallel tree contraction is a well established method of parallel tree processing. There are efficient and useful algorithms for binary trees, including the Shunt contraction algorithm and one based on the m-bridge decomposition method. However, for trees of unbounded degree, there are few practical tree contraction algorithms. The standard approach is “binarization, ” namely to translate the input tree to a full binary tree beforehand. To prevent the overhead introduced by binarization, we previously proposed the Rake-Shunt contraction algorithm (ICCS 2011), which is a generalization of the Shunt contraction algorithm to trees of unbounded degree. This paper further extends this result. The major contribution is to show that the Rake-Shunt contraction algorithm is a tree contraction algorithm that uses fewer types of primitive contraction operations if we assume the input tree has been binarized. This observation clarifies the connection between the Rake-Shunt contraction algorithm and those based on binarization. In particular, it enables us to translate a parallel program developed based on the Rake-Shunt contraction algorithm to one based on the m-bridge decomposition method. Thus, we can choose whether to use binarization according to the situation.