  The singularity structure of many IIB supergravity solutions asymptotic to
$AdS_5 \times S^5$ becomes clearer when one considers the full ten dimensional
solution rather than the dimensionally reduced solution of gauged supergravity.
It has been shown that all divergences in the gravitational action of the
dimensionally reduced spacetime can be removed by the addition of local
counterterms on the boundary. Here we attempt to formulate the counterterm
action directly in ten dimensions for a particular class of solutions, the
${\cal N} = 0$ Polchinski-Strassler solutions, which are dual to an ${\cal N}
=4$ SYM theory perturbed by mass terms for all scalars and spinors. This
involves constructing the solution perturbatively near the boundary. There is a
contribution to the Weyl anomaly from the mass terms (which break the classical
conformal invariance of the action). The coefficient of this anomaly is
reproduced by a free field calculation indicating a non-renormalisation theorem
inherited from the ${\cal N} =4$ theory. We comment on the structure of the
full solutions and their construction from uplifting particular $ {\cal N} = 0$
flows in five dimensions.
