Neutron streaming through the gap between a port plug and the port walls will be a major contributor to the shutdown dose rate in ITER, and calculating this streaming requires very effective variance reduction. The article describes a way of estimating importances for a calculation of the fast neutron flux, which will then generate weight windows. If necessary, these can be refined iteratively. Once the fast neutron calculation works well, the weight windows can be extended to lower energies and to photons using appropriate factors for which some values are suggested here. Again, these weight windows can be improved iteratively. Test runs in a simplified geometry performed fairly well, though optimizing performance simultaneously for the gamma flux at the end of the port and above it is difficult.