  We consider, in 5 dimensions, the low energy effective action induced by
heterotic string theory including the leading stringy correction of order
alpha'. In the presence of a single positive tension flat brane, and an
infinite extra dimension, we present a particular class of solutions with
finite 4-dimensional Planck scale and no naked singularity. A ``self-tuning''
mechanism for relaxing the cosmological constant on the brane, without a
drastic fine tuning of parameters, is discussed in this context. Our solutions
are distinct from the standard self-tuning solutions discussed in the context
of vanishing quantum corrections in alpha', and become singular in this limit.
