  We show that the classical cosmological constant in type II flux
compactifications can be written as a sum of terms from the action of localized
sources plus a specific contribution from non-trivial background fluxes.
Exploiting two global scaling symmetries of the classical supergravity action,
we find that the flux contribution can in many interesting cases be set to zero
such that the cosmological constant is fully determined by the boundary
conditions of the fields in the near-source region. This generalizes and makes
more explicit previous arguments in the literature. We then discuss the problem
of putting \bar{D3}-branes at the tip of the Klebanov-Strassler throat glued to
a compact space in type IIB string theory so as to engineer a de Sitter
solution. Our result for the cosmological constant and a simple global argument
indicate that inserting a fully localized and backreacting \bar{D3}-brane into
such a background yields a singular energy density for the NSNS and RR 3-form
field strengths at the \bar{D3}-brane. This argument does not rely on partial
smearing of the \bar{D3}-brane or a linearization of field equations, but on a
few general assumptions that we also discuss carefully.
