We analyze the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading (ln N/N) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit (N -->infinity), we estimate the free energy of a defect-free crystal of particles interacting through an r(-12) potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at rho sigma(3) = 1.0409, the excess free energy of a defect-free hard-sphere crystal is 5.918 89(4)kT per particle. This, however, is not the free energy of an equilibrium hard-sphere crystal. The presence of a finite concentration of vacancies results in a reduction of the free energy that is some two orders of magnitude larger than the present error estimate. (C) 2000 American Institute of Physics. [S0021-9606(00)50912-X].