Due to persistent ionospheric current systems at high latitudes, satellite magnetic measurements have high noise levels in the Polar regions. Consequently, small-scale lithospheric features are much more difficult to resolve there than at lower latitudes. Using linear combinations of spherical harmonics (SH), we define localized functions which are band-limited to a given maximum degree. Thus, a model's SH resolution can be varied over the globe. We produce a lithospheric field model from CHAMP satellite data which resolves features to SH degree 90 at low latitudes, but only to SH degree 60 in the Polar regions. The new model can be downward continued from satellite altitude to the Earth's surface without generating spurious high-latitude anomalies.