Rigorous variational upper bounds are presented for the effective bed emissivity is an element of(eff) of a model semi-infinite fiber bed made up of long, parallel, randomly placed, freely overlapping cylinders for two possible bed edges-fibers perpendicular and fibers parallel to the bed edge. Calculations of bed emissivity variational results for both cases provide significant improvement over first-order scattering upper bounds given in a previous paper. For high void fraction Phi -> 1 and fiber surface emissivity values of epsilon(s), = 0. 5, 0.3, and 0. 1, respective bed emissivity upper bound reduction improvements of 4.14, 12.2, and 35.8% were generated for the latter bed edge structure, and 4.08, 11.3, and 32.2% were obtained for the former case. Along with the first-order scattering lower bounds on epsilon(eff), improved estimates of bed emissivities were calculated for high-temperature, nonmetallic fiber beds with epsilon(s) >= 0.55. Bed emissivity enhancement factors (epsilon(eff)/epsilon(s)) of 1.27 for fibers parallel to the semi-infinite bed edge and 1.42 for fibers perpendicular to the bed edge were observed for high fiber bed porosity Phi = 0.9 and epsilon(s) = 0.55. Results compared favorably with an experimental correlation and Monte Carlo simulations.