We present a new distributed algorithm for state space minimization modulo branching bisimulation. Like its predecessor it uses signatures for refinement, but the refinement process and the signatures have been optimized to exploit the fact that the input graph contains no tau-loops. The optimization in the refinement process is meant to reduce both the number of iterations needed and the memory requirements. In the former case we cannot prove that there is an improvement, but our experiments show that in many cases the number of iterations is smaller. In the latter case, we can prove that the worst case memory use of the new algorithm is linear in the size of the state space, whereas the old algorithm has a quadratic upper bound. The paper includes a proof of correctness of the new algorithm and the results of a number of experiments that compare the performance of the old and the new algorithms.