Stress inversion from fault/slip data is an important modern technique for structural geologists. The parameter (or sigma) space may be reduced from five to three dimensions if an Andersonian stress state (having a vertical principal direction) is assumed. In such a case, associated fault/slip data can be displayed after some transformation on a stereonet. Homogeneous fault/slip data tend to lie in a great circle, while heterogeneous data lie in no less than two great circles. Visual appreciation thus becomes fairly easy, in particular, separation of the heterogeneous fault/slip data set into many homogeneous subsets. The unit vectors normal to the great circles are the solutions giving the controlling reduced stress vectors (v). Permitted solutions to a homogeneous set or subset are v and -v. The acceptability of each solution depends upon the fit between calculated and measured fault slip senses. Several examples of applications of this method are used for its validation. These examples also illustrate the potential value of the method in making a rough, simple and visual appreciation of fault/slip data under approximately Andersonian stress. We believe the method will have a broad applicability as Andersonian stress represents the ideal states for the various tectonic regimes.