Satellite magnetometry is plagued by the Backus effect which renders maps of the magnetic field derived from measurements of the total field intensity unreliable, especially near the geomagnetic equator. The only remedy is to use oriented, vector component data in addition to scalar intensity data, but this requires either accurate determination of the satellite attitude or the use of data from permanent magnetic observatories. The former adds considerably to the cost and complexity of satellite magnetometry; the latter suffers in practice from the poor geographical distribution of magnetic observatories. Here we re-examine the problem of attitude determination, and ask how well the attitude needs to be determined to alleviate the Backus effect. We show that the use of a more complete model of the errors in satellite vector component data allows the requirements on attitude determination to be relaxed significantly, so that lower-cost means of obtaining attitude determination, such as GPS, can be employed. ¿ American Geophysical Union 1995