First-collision probabilities for a regular lattice of cylindrical fuel rods and moderator are calculated using the assumption that neutrons reaching the outer boundary of the unit cell are returned isotropically. Comparisons are made with results using Fukai's exact method and other approximate methods. The collision probabilities are used in calculating thermal-disadvantage factors which are compared with those from discrete-ordinate calculations using various boundary conditions. The treatment is extended to lattices with cladding on the fuel, and average thermal fluxes are compared with those computed by the THERMOS code. Collision probabilities calculated by the method presented here are in rather good agreement with exact values.