  We propose a new mechanism that adapts to string theory a perturbative method
for stabilizing moduli without leaving the domain of perturbative control,
thereby evading the `Dine-Seiberg' problem. The only required nonperturbative
information comes from the standard renormalization-group resummation of
leading logarithms that allow us simultaneously to work to a fixed order in the
perturbative parameter $\alpha$ and to all orders in $\alpha \ln\tau$ where
$\tau$ is a large extra-dimensional modulus. The resulting potential is
naturally minimized for moduli of order $\tau\sim e^{1/\alpha}$ and so can be
exponentially large given ${\cal O}(10)$ input parameters. The mechanism relies
on accidental low-energy scaling symmetries known to be generic and so is
robust against UV details. The resulting compactifications generically break
supersymmetry and 4D de Sitter solutions are relatively easy to achieve without
additional uplifting. Variations on the theme lead to inflationary scenarios
for which the size of the stabilized moduli differ significantly before and
after inflation and so provide a dynamical mechanism whereby inflationary
scales are much larger than late-time physical ($e.g.$~supersymmetry breaking)
scales, with this hierarchy contingent on past cosmic evolution with the
inflaton playing a secondary late-time role as a relaxation field. We apply
this formalism to warped $\hbox{D3}$-$\overline{\hbox{D3}}$ inflation using
non-linearly realized supersymmetry to describe the antibrane tension and the
Coulomb interaction, and show how doing so our perturbative modulus
stabilization mechanism evades the $\eta$-problem that usually plagues this
scenario. We speculate about the relevance of our formalism to tachyon
condensation at later stages of brane-antibrane annihilation.
