First of all, we would like to thank both D. Woodard and M. Girolami & A. Mira for their excellent and detailed comments on our paper. Their remarks and questions have given us quite a number of new ideas for improving our sampling procedure. As suggested by both, we have conducted new sampling runs for two additional examples, which illustrate the usefulness of CIMH and ACIMH and answer some of the ques- tions brought forward. Since Woodard’s comments focus on one particular aspect of CIMH/ACIMH, while Girolami & Mira point out several different considerations, we will first reply to Woodard’s comments.