The complexity of pairwise RNA structure alignment depends on the structural restrictions assumed for both the input structures and the computed consensus structure. For arbitrarily crossing input and consensus structures, the problem is NP-hard. For non-crossing consensus structures, Jiang et al's algorithm  computes the alignment in O(n 2 m 2) time where n and m denote the lengths of the two input sequences. If also the input structures are non-crossing, the problem corresponds to tree editing which can be solved in O(m2n(1 + log n/m))time . We present a new algorithm that solves the problem for d-crossing structures in O(d m 2 nlogn) time, where d is a parameter that is one for non-crossing structures, bounded by n for crossing structures, and much smaller than n on most practical examples. Crossing input structures allow for applications where the input is not a fixed structure but is given as base-pair probability matrices.