Statistical data show that it is much less expensive to correct software bugs at the early design stage rather than the late stage of the development process when the final system has already been implemented and integrated together. The use of slicing and execution histories as an aid in software debugging is well established for programming languages like C and C++; however, it is rarely applied in the field of software design specification. We propose a solution by applying the source code level technologies to debugging software designs represented in a high-level specification and description language such as SDL. More specifically, we extend execution slice-based heuristics from source code-based debugging to the software design specification level. Suspicious locations in an SDL specification are prioritized by their likelihood of containing faults. Locations with a higher priority should be examined first rather than those with a lower priority as the former are more likely to contain the faults. A debugging tool, SmartD_SDL, with user-friendly interfaces was developed to support our method. An illustration is provided to demonstrate the feasibility of using our method to effectively debug an architectural design.