Geomagnetic field models computed from intensity measurements on or near the Earth's surface are plagued with strong errors known as the Backus effect. These errors are related to the mathematical non-uniqueness of the solution which can be theoretically removed by the knowledge of the dip-equator location. Here, we present a new method for computing models using intensity data and additional information about the location of the dip-equator. We first give a numerical validation of this approach in an ideal case in which the dip-equator can be assumed to be perfectly located. We then show that in practice, updating a good past model of the field with a model of secular variation can constrain the location of the dip-equator sufficiently for our method to be useful. Implications for the planning of future satellite missions are briefly discussed. ¿ 1998 American Geophysical Union