  Continuing the programme of constructing the backreacted solution
corresponding to smeared anti-D3 branes in the warped deformed conifold, we
solve analytically the equations governing the space of first-order
deformations around this solution. We express the results in terms of at most
three nested integrals. These are the simplest expressions for the space of
$SU(2) \times SU(2) \times \ZZ_2$-invariant deformations, in which the putative
solution for smeared anti-D3 branes must live. We also explain why one cannot
claim to identify this solution without fully relating the coefficients of the
infrared and ultraviolet expansions of the deformation modes. The analytic
solution we find is the first step in this direction.
