In this paper we unify two approaches to determining magnetopause shape and location from observations by fitting one model simultaneously to both the crossing data and the calculated data of magnetopause flaring angle, to achieve more accurate magnetopause shapes. We prepare two magnetopause models, each of which is an ellipsoid from the subsolar point to the position where the distance of the ellipsoid from the X axis is maximum. The model magnetopause beyond this position is a cylinder attached to the edge of the ellipsoid at this location. This choice of shapes makes it easier to compare our results with earlier work which fit ellipsoids to (only) crossing data. In one of our two models, the focus of the ellipsoid lies at the center of the Earth, whereas in the other it lies at a position determined from fits to the data. We use a statistical criterion (called AIC) that lets us objectively determine which model better fits the data. As a result, we find that a model with an off-center focus better expresses the nature of the observed data. Despite differing mathematical formulations, our model results generally resemble those of Petrinec and Russell [1996>. Consequently, the mathematical expression is not the major reason why these models flare more (less) than the model of Roelof and Sibeck [1993> for very small (large) solar wind dynamic pressure. ¿ 1999 American Geophysical Union