•Two variants of Sendys to patch its NOR problem and improve its performance.•First comprehensive theoretical analysis on Sendys and its variants.•A short-cut reformulation of the enhanced Sendys with the best performance.•Empirical studies on single and multiple faults to complement theoretical analysis. Combining spectrum-based fault localization (SBFL) with other techniques is generally regarded as a feasible approach as advantages from both techniques would be preserved. Sendys which combines SBFL with slicing-hitting-set-computation is one of the promising techniques. However, all current evaluations on Sendys were obtained via empirical studies, which have inevitable threats to validity. Besides, purely empirical studies cannot reveal the essential reason that why Sendys performs well or badly, and whether all the complicated computations are necessary. Therefore, in this paper, we provide an in-depth theoretical analysis on Sendys, which can give definite and convincing conclusions. We generalize our previous theoretical framework on SBFL, to make it applicable to combined techniques like Sendys. We first provide a variant of current Sendys by patching its loophole of ignoring “zero or negative risk values” in normalization. This variant plays as a substitution of the original Sendys, as well as one of the baselines in our analysis. Then, by modifying a few steps of this variant, we propose an enhanced Sendys and theoretically prove its superiority over several other methods in single-fault scenario. Moreover, we provide a short-cut reformulation of the enhanced Sendys by preserving its performance, but only requiring very simple computations. And it is proved to be even better than traditional SBFL maximal formulas. As a complementary, our empirical studies with 13 subject programs demonstrate the obvious superiority of the enhanced Sendys, as well as its stability across different formulas in single-fault scenario. For multiple-fault cases, the variant of Sendys is observed to have the best performance. Besides, this variant has shown great helpfulness in improving the bad performance of the original Sendys when encountering the NOR problem.