In this paper we present polynomial time algorithms deciding branching bisimilarity between finite-state systems and several classes of infinite-state systems: BPA and normed BPP. The algorithm for BPA improves a previous one given by Kuˇcera and Mayr, while the one for normed BPP demonstrates the polynomial-time decidability of the problem, which is unknown previously. The proof style follows an early work of Kuˇcera and Mayr, where similar results for weak bisimilarity are established.