  Analysing the static, spherically symmetric graviton-dilaton solutions in low
energy string and Brans-Dicke theory, we find the following. For a charge
neutral point star, these theories cannot predict non trivial PPN parameters,
$\beta$ and $\gamma$, without introducing naked singularities. We then couple a
cosmological constant $\Lambda$ as in low energy string theory. We find that
only in low energy string theory, a non zero $\Lambda$ leads to a curvature
singularity, which is much worse than a naked singularity. Requiring its
absence upto a distance $r_*$ implies a bound $| \Lambda | < 10^{- 102}
(\frac{r_*}{{\rm pc}})^{- 2}$ in natural units. If $r_* \simeq 1 {\rm Mpc}$
then $| \Lambda | < 10^{- 114}$ and, if $r_* \simeq 10^{28} {\rm cm}$ then $|
\Lambda | < 10^{- 122}$ in natural units.
