The decay of mounds about a dozen layers high on the Si(1 1 1)7 x 7 surface [Surf. Sci. Rep. 34 (1999) 171] has been measured quantitatively by scanning tunneling microscopy and compared with analytic predictions for the power-law dependence on time predicted for a step-mediated decay mechanism [Mater. Res. Sec. Symp. Proc. 528 (1998) 237]. In accordance with these predictions, we find [Phys. Rev. Lett. 84 (2000) 3662] an exponent 1/4 associated with the (3D) decay of the mound height and exponent 1/3 associated with the (2D) decay of top-layer islands, appropriate to diffusion-limited behavior. The detailed effects of atomic-scale behavior at the step edges enter as the product of step stiffness and mobility; the measured value is consistent with earlier observations [http://www] of decay of single-layer structures. Using parameters from a continuum step model [Phys. Rev. Lett. 80 (1998) 552]. we capture the essence of the kinetics. Qualitative features distinguish these mounds from multi-layer islands found on metals such as Cu(1 1 1).