The double heterogeneity of the core of pebble bed-type high-temperature reactors (HTRs) requires special attention when lattice codes are applied to a unit cell of such systems. As the self-shielding of the resonance absorption takes place in the small fuel grains in the pebbles, the grain-lattice calculation should apply a Dancoff factor for the grain lattice yet take into account the finiteness of the grain lattice in a pebble and the possibility of a neutron reaching another pebble. In a study of HTR lattices, the Dancoff factor was calculated using the DANCOFF-MC program. For a finite lattice of fuel grains in the fuel region of a pebble, the space-dependent Dancoff factor was calculated, and it was averaged over the volume of the fuel in one pebble. This single-pebble Dancoff factor was further corrected to include the effect of other pebbles. The sensitivity of the Dancoff factor to core composition and the sensitivity of core calculations to the Dancoff factor are discussed, and a numerical example is given.