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A slow-group-velocity- and low-group-velocity-dispersion photonic crystal slab waveguide is designed by using capsule-shaped air holes in hexagonal lattice. The theoretical study shows that adjusting the aspect ratio of holes in the innermost rows can fine-tune the dispersion tail. The presented design can achieve nearly flat-band photonic crystal waveguides with group index of 21-36 over the normalized bandwidth (Deltaomega/ omega) of 1.38% - 0.4%. We also discuss the effects of the change in the holes' aspect ratio combined with a slight size adjustment. The group index in the range of 21-43 for normalized bandwidth of about 1.5% - 0.3% is obtained with the combination effect. The optimized designed exhibits a nearly constant group index of 21 over 22.7 nanometer bandwidth at lambda = 1.55 mum.