Recent studies of samples from seamounts indicate that the distribution of magnetic intensity is approximately lognormal, which implies that the commonly adopted models of interior magnetization based upon a constant vector with an isotropic perturbation are inappropriate. We develop a unidirectional model in which the direction of magnetization is fixed and the intensity is of one sign, with no upper limit on magnitude, which, if the seamount is built during a period of single magnetic polarity, is likely to be a better approximation. We show that models of this class fitting the data best in the two-norm sense conform to the ideal-body pattern comprising undirectional, point dipoles in the surface of the seamount. Practical methods are developed for discovering the best data misfit associated with paleopole position. The methods are first tested on simple artificial magnetic anomalies and are found to be capable of recovering the true pole position with high accuracy when such a solution is possible; also when a mixed polarity artificial model is analyzed, it is found that there are no unidirectional solutions, just as would be hoped. The method is next applied to three seamount surveys. In the first it is found that every direction of magnetization is in accord with the data, so that apparently nothing useful can be learned from the survey without a stronger assumption; this result is in contrast with the results of an earlier solution based upon a statistical model, which yielded a high accuracy in the position of the paleopole. The second investigation provides a reasonably compact location of the paleopole of the seamount. The third magnetic anomaly is complex and earlier studies concluded this was necessarily the product of mixed polarity magnetization. We find in fact unidirectional magnetizations can satisfy observation. ¿ American Geophysical Union 1991