**I** was recently asked to referee a PhD thesis at Institut Pasteur, written by Yannick Spill, in Bioinformatics which essentially focus on statistical and computational aspects. (Hence the request. The defence itself was today.) Among the several papers included in the thesis, there was this post-worthy paper called *A convective replica-exchange method for sampling new energy basins* written by Spill, Bouvier and Nilges and published in the *Journal of Computational Chemistry*, paper that extends the usual multiple tempering algorithm in a method called the convective replica exchange algorithm. Rather than selecting the chain to exchange at random, it forces a given chain to go through all temperature steps in a cyclic manner and only moves to another chain when the cycle is over. There is a delayed rejection flavour therein in that the method does not let go: it keeps proposing moves to the next level until one is accepted (hence earning from me the nickname of the pit-bull algorithm!). While the thesis includes a (corrected) proof of ergodicity of the method, I wonder if the proof could have been directly derived from a presentation of the algorithm as a reversible jump MCMC type algorithm (Green, 1995). The experiments presented in the paper are quite worthwhile in that they allayed my worries that this new version of replica exchange could be much slower than the original one, because of the constraint of moving a given chain to a given neighbouring level rather than picking those two entities at random. (Obviously, the performances would get worse with a sparser collection of inverse temperatures.) I am still uncertain however as to why compelling the exchange to take place in this heavily constrained way induces better dynamics for moving around the sampling space, my reasoning being that the proposals remain the same. However during the defence I realised that waiting for a switch would induce visiting more of the tails…