Compact spectrometers based on disordered planar waveguides exhibit a rather high resolution with a relatively small footprint compared to conventional spectrometers. This is achieved by multiple scattering of light, which — if properly engineered — significantly enhances the effectiveoptical path length. Here a design study of random spectrometers for TE- and TM-polarized light is presented that combines the results of Mie theory, multiple-scattering theory, and full electromagnetic simulations. It is shown that the performance of such random spectrometers depends on single-scattering quantities, notably on the overall scattering efficiency and the asymmetry parameter. Further, the study shows that a well-developed diffusive regime is not required in practice and that a standard integrated optical layout is sufficient to obtain efficient devices even for rather weakly scattering systems consisting of low index inclusions in high-index matrices, such as pores in planar silicon-nitride-based waveguides. This allows for both significant reductions in footprint with acceptable losses in resolution and for device operation in the visible and near-infrared frequency range.