The Dancoff correction for fuel rods surrounded by air gaps arranged in a hexagonal lattice in a moderator is calculated as a function of the rod radius measured in units of moderator mean free paths, the moderator to fuel volume ratio, and the width of the air gap relative to the radius of the rod. It is found that the Dancoff correction increases with the width of the air gap, when the other parameters are kept constant. This leads to a decrease of the mean chord length in the moderator and consequently a slight increase of the resonance escape probability, whose magnitude may be estimated from the simplest formula for the effective resonance integral.