  We investigate the effective conductivity ($\sigma_e$) of a class of
amorphous media defined by the level-cut of a Gaussian random field. The three
point solid-solid correlation function is derived and utilised in the
evaluation of the Beran-Milton bounds. Simulations are used to calculate
$\sigma_e$ for a variety of fields and volume fractions at several different
conductivity contrasts. Relatively large differences in $\sigma_e$ are observed
between the Gaussian media and the identical overlapping sphere model used
previously as a `model' amorphous medium. In contrast $\sigma_e$ shows little
variability between different Gaussian media.
