  It is generally believed that knowing the light travel time up to the
post-post-Minkowskian level (terms in $G^2$) is sufficient for modelling the
most accurate experiments designed to test general relativity in a foreseeable
future. However, we have recently brought a rigorous justification of the
existence of an enhanced term of order $G^3$ which becomes larger than some
first-order contributions like the gravitomagnetic effect due to the rotation
of the Sun or the solar quadrupole moment for light rays almost grazing the
solar surface. We show that this enhanced term must be taken into account in
solar system experiments aiming to reach an accuracy less than $10^{-7}$ in
measuring the post-Newtonian parameter $\gamma$.
