  Black holes supported by self-interacting conformal scalar fields can be
considered as renormalizably dressed since the conformal potential is nothing
but the top power-counting renormalizable self-interaction in the relevant
dimension. On the other hand, potentials defined by powers which are lower than
the conformal one are also phenomenologically relevant since they are in fact
super-renormalizable. In this work we provide a new map that allows to build
black holes dressed with all the (super-)renormalizable contributions starting
from known conformal seeds. We explicitly construct several new examples of
these solutions in dimensions $D=3$ and $D=4$, including not only stationary
configurations but also time-dependent ones.
