We consider the problem of constructing a time-dependent map of the magnetic field at the core-mantle boundary. We use almost all the available data from the last 300 years to produce two maps, one for the period 1690--1840 and the other for 1840--1990. We represent the spatial dependency of the field using spherical harmonics, the time dependency using a cubic B-spline basis, and seek the smoothest solutions compatible with the observations. Particular attention must be paid to the effects of the crustal field in the data. We argue that for observations from permanent magnetic observatories the most efficient strategy is to use first-differences of annual means; for satellite data the most efficient strategy is simply to limit the number of data used so as to minimize any tendency to map the crustal field into the core field. The resulting model fits the observatory data better than any previous model yet has less power in the secular variation than previous models, demonstrating that very simple models fit the data. The resulting time-dependent field map exhibits much of the same structure in the field and its secular variation identified in earlier studies. ¿ American Geophysical Union 1992