  We examine to what extent perturbative alpha'-corrections can generate a
small cosmological constant in warped string compactifications. Focusing on the
heterotic string at lowest order in the string loop expansion, we show that,
for a maximally symmetric spacetime, the alpha'-corrected 4D scalar potential
has no effect on the cosmological constant. The only relevant terms are instead
higher order products of 4D Riemann tensors, which, however, are found to
vanish in the usual perturbative regime of the alpha'-expansion. The heterotic
string therefore only allows for 4D Minkowski vacua to all orders in alpha',
unless one also introduces string loop and/or nonperturbative corrections or
allows for curvatures or field strengths that are large in string units. In
particular, we find that perturbative alpha'-effects cannot induce weakly
curved AdS_4 solutions.
