There is lack of agreement on the underlying cause of widely observed power-law scaling behaviour of magnetic-anomaly fields. Some workers ascribe this behaviour to intrinsic 3-D fractal distributions of magnetization in the crust of the Earth; others point to a power-law exponent β∼ 3, expected for a random ensemble of statistically independent magnetized prisms: the classic Spector & Grant model (SG model). We apply a perturbation approach to the Parker model to derive expressions for the power spectra of magnetic-anomaly fields in the presence of laterally varying magnetization and/or topography at the top of magnetic basement. Under appropriate assumptions, our modified Parker model reduces to either an SG model or a 2-D fractal model. In the case of fractal magnetization without topography, the power-law slope of the magnetic-anomaly field (after depth correction) is equal to the power-law slope for the magnetization distribution. In the case of fractal basement topography alone, the power-law slope is reduced by 2. Where both the magnetization and topography are fractal, the effects of magnetization tend to dominate the power-law behaviour of the associated magnetic-anomaly field. Two real-data examples from the Canadian Shield exhibit power-law exponents of 2.02 ± 0.02 and 1.42 ± 0.01, within a wavelength band of 2 to 100 km. These slopes are significantly different from previously cited values of ∼3, casting doubt on the general applicability of the β∼ 3 slope that is inherent to SG models at high wavenumber.