We define the concepts of z-sets and z-detections for combinational circuits (or the combinational logic of scan circuits). Based on these concepts we define structural characteristics and characteristics based on fault simulation. We show that these characteristics determine the numbers of fault pairs that are guaranteed to be distinguished by a given fault detection test set. These fault pairs do not need to be considered during diagnostic fault simulation or test generation. We demonstrate that benchmark circuits as well as industrial circuits have these characteristics to a larger extent than may be expected. As a result, only small percentages of fault pairs need to be considered during diagnostic fault simulation or test generation once a fault detection test set is available. In addition, these fault pairs can be identified efficiently.