Superposition of the magnetic fields of core and crustal origin causes problems in studying both the dynamo and near-surface magnetic sources: short wavelength features of the core field are lost beneath the crustal signal, whereas large-scale features of the crustal field are similarly overpowered by the core field. We attempt to place upper and lower bounds on the power in the long wavelength part of the crustal field so as to quantify the degree of possible contamination of the large-scale core field. Upper bounds are calculated by limiting the maximum permissible intensity of magnetisation of crustal rocks. To find lower bounds, we assume the high spherical harmonic degree ( l > 15) power is entirely crustal in origin and adopt a simple stochastic model which can account for this power. The model takes the magnetisation of the crust to be a realisation of a zero-mean, stationary, isotropic, random process. We examine several pertinent ensembles of observations to try to ascertain the underlying probability distribution function of the random process. The results are equivocal, but the original Gaussian distribution assumption of Jackson (1990, Geophys. J. Int., 103: 657-673) may be suboptimal. We use the model to place a lower bound on the low degree power in the crustal field which is masked by the main field, by restricting the coherence between magnetisation to decrease as a function of site separation, a condition thought to be reasonable for the Earth. At the present level of accuracy of the power spectrum the lower bound is, disappointingly, rather small. Similarly, the upper bounds are, predictably, rather large.