A comprehensive analysisof rock structures in non-oriented (axially oriented) drillcore is now available (Laing, in press). The system embodies new concepts which better equip the geologist and engineer to deal from the outset with optimising the acquisition of structural information in drillcore, logging, interpreting, and graphically presenting the results. The few existing techniques for determining orientations of structures are augmented by a wide range of new techniques, and all are brought together into two solution types by considering the underlying Euclidean geometries. Analysis of these solution types in terms of what data are required to implement each solution and what assumptions need to be made, leads to strategies which facilitate intelligent design of different drilling programs for blind and outcropping situations. Drillcorc is variably structurally fertile, depending on the number of different structures present. This concept fosters the selective logging only of the more fertile core. Drillholes are also variably fertile, depending on their orientational relationship to the structures in the host rocks. Structural parameters are either vectorial or non-vectorial. Vectorial structures parameters comprise normal structural orientations plus polar vectors like vergence, younging, shear sense and so on. They can be determined by one of two solution types: external solutions, which use an external reference structure to fix the drillcore and thus permit orientation of all structures within that core, and internal solutions, which use orientational data from a selected structure at three or more different drillhole orientation to determine the unique orientation of that structure, without reference to any external structure.