  We present the current status of a revised strategy to compute the running of
renormalized quark masses in QCD with three flavours of massless O(a) improved
Wilson quarks. The strategy employed uses the standard finite-size scaling
method in the Schr\"odinger functional and accommodates for the
non-perturbative scheme-switch which becomes necessary at intermediate
renormalized couplings as discussed in [arXiv:1411.7648].
