  In order for a modified gravity model to be a candidate for cosmological dark
energy it has to pass stringent local gravity experiments. We find that a
Brans-Dicke (BD) theory with well-defined second order corrections that include
the Gauss-Bonnet term possess this feature. We construct the generic second
order theory that gives, to linear order, a BD metric solution for a point-like
mass source. We find that these theories interpolate between general relativity
(GR) and BD gravity. In particular it is found that the relevant Eddington
parameter, that is commonly heavily constrained by time delay experiments, can
be arbitrarily close to the GR value of 1, with an arbitrary BD parameter. We
find the region where the solution is stable to small timelike perturbations.
