Before it becomes a sensitive probe of the epoch of reionization, the dark ages and fundamental physics, 21-cm tomography must successfully contend with the issue of foreground contamination. Broad-band foreground sources are expected to be roughly 4 orders of magnitude larger than any cosmological signals, so precise foreground models will be necessary. Such foreground models often contain a large number of parameters, reflecting the complicated physics that governs foreground sources. In this paper, we concentrate on spectral modelling (neglecting, for instance, bright point source removal from spatial maps) and show that 21-cm tomography experiments will likely not be able to measure these parameters without large degeneracies, simply because the foreground spectra are so featureless and generic. However, we show that this is also an advantage, because it means that the foregrounds can be characterized to a high degree of accuracy once a small number of parameters (likely three or four, depending on one’s instrumental specifications) are measured. This provides a simple understanding for why 21-cm foreground subtraction schemes are able to remove most of the contaminants by suppressing just a small handful of simple spectral forms. In addition, this suggests that the foreground modelling process should be relatively simple and will likely not be an impediment to the foreground subtraction schemes that are necessary for a successful 21-cm tomography experiment.