In the paper describing MrBayes 3.2, there is the following phrase:
MrBayes 3.2 further includes a completely new type of tree proposal
that is guided using parsimony scores. The details of the
parsimony-biased proposals will be presented elsewhere; however,
tentative empirical results show that they can improve the speed of
convergence by an order of magnitude on some problems (see also Höhna
and Drummond 2012).
Can someone point me to this paper? I'd like to read about them! (@Alexis_RAxML, I'm assuming that you learned about then from just reading the MB source?)