The single-scattering properties of concave fractal polyhedra are investigated, with particle size parameters ranging from the Rayleigh to geometric-optics regimes. Two fractal shape parameters, irregularity and aspect ratio, are used to iteratively construct “generations” of irregular fractal particles. The pseudospectral time-domain (PSTD) method and the improved geometric-optics method (IGOM) are combined to compute the single-scattering properties of fractal particles over the range of size parameters. The effects of fractal generation, irregularity, and aspect ratio on the single-scattering properties of fractals are investigated. The extinction efficiency, absorption efficiency, and asymmetry factor, calculated by the PSTD method for fractal particles, with small-to-moderate size parameters, smoothly bridges the gap between those size parameters and size parameters for which solutions given by the IGOM may be used. Somewhat surprisingly, excellent agreement between values of the phase function of randomly oriented fractal particles calculated by the two numerical methods is found, not only for large particles, but in fact extends as far down in equivalent-projected-area size parameters as 25. The agreement in the case of other nonzero phase matrix elements is not as good at so small a size. Furthermore, the numerical results of ensemble-averaged phase matrix elements of a single fractal realization are compared with dust particle measurements, and good agreement is found by using the fractal particle model to represent data from a study of feldspar aerosols.