  We revisit the renormalization of Phi-derivable approximations from a
slightly different point of view than the one which is usually followed in
previous works. We pay particular attention to the question of the existence of
a solution to the self-consistent equation that defines the two-point function
in the Cornwall-Jackiw-Tomboulis formalism and to the fact that some of the
ultraviolet divergences which appear if one formally expands the solution in
powers of the bare coupling do not always appear as divergences at the level of
the solution itself. We discuss these issues using a particular truncation of
the Phi functional, namely the simplest truncation which brings non-trivial
momentum and field dependence to the two-point function.
