Monte Carlo calculations are performed for a full-coverage spherical system consisting of a stainless steel first wall and a lead-beryllium neutron multiplier. All the calculations use the MORSE-CG code, employing the Los Alamos National Laboratory 30-group neutron cross-section set CLAW-IV in P3 approximation. For multiplier thicknesses varying from 3 to 22.5 cm, the ratio of neutrons leaking from the system with and without 1.5-cm-thick stainless steel decreases from 1.48 to 1.41 for lead and from 1.78 to 1.58 for beryllium. For a three-region system consisting of a first wall, multiplier, and a homogeneous mixture of water and natural lithium, the tritium breeding ratio for the stainless steel-beryllium-homogeneous (natural lithium + water) system is only ∼9% more than that of the stainless steel-lead-homogeneous (natural lithium + water) system. Recent measurements and calculations on neutron multiplication suggest a downward correction for Be(n,2n) and an upward correction for Pb(n,2n) in the ENDF/B-IV cross-section set. In light of such changes in cross sections, a comparison is made between beryllium and lead as a multiplier with a stainless steel first wall.