Dynamic slicing and its underlying dynamic dependence analysis have been extensively studied and used as the foundation for numerous automated-debugging techniques. One limitation of dynamic slicing, when used for debugging, is that it only considers program dependences that are actually observed during the execution(s) of interest. Some faults, however, involve potential, rather than actual dependences-dependences that would be observed if the correct program was executed but are missing when the faulty program is executed. In particular, traditional dynamic slicing may fail to locate faults that involve assignments that should have occurred in a correct execution and did not occur in the failing execution being debugged. Relevant slicing techniques partially address this problem by identifying missing assignments due to incorrect control-flow. However, they do not consider the case of assignments that do occur but modify the wrong memory location (e.g., the wrong element of an array). Debugging techniques based on existing dynamic slicing approaches may therefore miss faults in the presence of this kind of incorrect assignments. To address this problem, we introduce the concept of potential memory-address dependence (PMD). Intuitively, PMDs represent the dependence relationship between an instruction s that affects the computation of a memory-address ma (e.g., by defining an array index or a pointer offset) and memory read instructions that are not observed to be dependent on s but could be affected by s (i.e., access the memory at ma) in a counterfactual execution of s. We also present a technique that computes PMDs and represents them on standard dynamic dependence graphs. To assess the effectiveness of our technique for debugging, we implemented PMD-Slicer, a dynamic slicer that accounts for PMDs, and performed an empirical evaluation on a benchmark of 364 real faults and 880 fault-revealing test cases. Our results are promising, in that almost 10% of the failing tests contained cases in which PMD-Slicer generated slices that included the corresponding fault, while a traditional dynamic slicer did not. Furthermore, considering PMDs only moderately increased slice sizes.