  Static solutions with a bulk dilaton are derived in the context of six
dimensional warped compactification. In the string frame, exponentially
decreasing warp factors are identified with critical points of the low energy
$\beta$-functions truncated at a given order in the string tension corrections.
The stability of the critical points is discussed in the case of the first
string tension correction. The singularity properties of the obtained solutions
are analyzed and illustrative numerical examples are provided.
