  We consider deformations of the singular "global cosmic string"
compactifications, known to naturally generate exponentially large scales. The
deformations are obtained by allowing a constant curvature metric on the brane
and correspond to a choice of integration constant. We show that there exists a
unique value of the integration constant that gives rise to a nonsingular
solution. The metric on the brane is dS_4 with an exponentially small value of
expansion parameter. We derive an upper bound on the brane cosmological
constant. We find and investigate more general singular solutions---``dilatonic
global string" compactifications---and show that they can have nonsingular
deformations. We give an embedding of these solutions in type IIB supergravity.
There is only one class of supersymmetry-preserving singular dilatonic
solutions. We show that they do not have nonsingular deformations of the type
considered here.
