Monte Carlo (MC) simulations were used to study the screened interactions between charged spherical macroions surrounded by discrete counterions, and to test previous theories of screening. The simulations were performed in the primitive cell of the bcc lattice, and in the spherical Wigner-Seitz cell that is commonly used in approximate calculations. We found that the Wigner-Seitz approximation is valid even at high volume fractions phi and large macroion charges Z, because the macroion charge becomes strongly screened. Pressures calculated from Poisson-Boltzmann theory and local density functional theory deviate from MC values as phi and Z increase, but continue to provide upper and lower bounds for the MC results. While Debye-Huckel (DH) theory fails badly when the bare charge is used, MC pressures can be fit with an effective DH charge, Z(DH), that is nearly independent of volume fraction. As Z diverges, Z(DH) saturates at z psi(max)R(m)/lambda, where z is the counterion charge, R(m) is the macroion radius, lambda is the Bjerrum length, and psi(max) is a constant of order 10.