We report Monte Carlo studies of solid-fluid coexistence for the soft-sphere potential: (r)=(r)n. Applying a recently developed integration method that proceeds along a coexistence line, we determined coexistence for essentially a continuum of softness s1n from s=0 (hard spheres) to ca. s=0.25. For s<0.16, we estimate that fcc is the stable crystal, and that bcc is stable for softer potentials; however, this result is not conclusive. We find substantial disagreement with early coexistence data for n=12, 9, 6, and 4, while confirming more recent studies for n=12 and 6. © 1994 The American Physical Society.