Natural porous media with a complex geometry can be simulated by a simple algorithm which ‘deposits’ grains of two different sizes on a cubic lattice. A relaxation process allows the grains to rearrange into a more stable configuration. The shapes and sizes of the two different grain types and the proportion in which they are mixed determine the pore structure. In the present work we have studied two different variations of the model: (1) a mixture of small grains of size the unit cube with fraction p and large grains with dimension 2 × 1 × 1 with fraction (1−p); (2) a mixture of small grains of size the unit cube with fraction p and large grains with dimension 3 × 1 × 1 with fraction (1−p). p is varied from 0 to 1. In both cases we calculate the conductivity of the porous medium generated when a conducting fluid fills the pore space and the solid matrix is insulating. We find that in this relaxed bidisperse ballistic deposition model, porosity and conductivity show interesting and, in some cases, non-monotonic variation with p. Both properties depend strongly on the size of the larger grain. Moreover, the conductivity curve may not follow the porosity curve faithfully, indicating a highly complex nature of the pore space.