The geomagnetic field at a given epoch can be used to partition the surface of the liquid outer core into a finite number of contiguous regions in which the radial component of the magnetic flux density, Br, is of one sign. These flux patches are instrumental in providing detail to surface fluid flows inferred from the changing geomagnetic field and in evaluating the validity of the frozen-flux approximation on which such inferences rely. Most of the flux patches in models of the modern field are small and enclose little flux compared to the total unsigned flux emanating from the core. To demonstrate that such patches are not required to explain the most spatially complete and accurate data presently available, those from the Magsat mission, I have constructed a smooth core field model that fits the Magsat data but does not possess small flux patches. I conclude that our present knowledge of the geomagnetic field does not allow us to resolve these features reliably at the core-mantle boundary; thus we possess less information about core flow than previously believed. ¿ American Geophysical Union 1996