In numerous cases, the use of standard methods of palaeostress inversion from fault slip data is prevented by the absence of structures that indicate the direction of slip on the fault. In such instances, however, the offset of planar markers, such as beds matched in the footwall and hanging wall, often allows the sense of dip separation (normal or reverse) to be observed. Where such displaced markers are horizontal or at least where their cut off lines are horizontal, it can be readily demonstrated that the sense of the dip-slip component of net slip is the same as the sense of dip separation. Ways are explored for characterizing the stress tensor from data consisting of the orientations of a collection of faults, each with known dip-slip sense (normal or reverse). On the basis of properties of the stress quadric the relationship between dip-slip sense, fault plane orientation, and the stress tensor is discovered. This relationship is used as the basis of a grid search method of stress inversion, in which a large number of stress tensors differing in orientation and shape are systematically considered. Those tensors that successfully explain the senses of offset on the observed faults are considered potential solutions to the palaeostress problem. Examples of different applications of the new stress inversion method are described, including the analysis of fault data from boreholes. These examples illustrate the way the new method potentially broadens the scope of palaeostress analysis. ¿ 2001 American Geophysical Union