An important cause of miscarriages of justice is the failure of crime investigators and lawyers to consider important plausible explanation for the available evidence. Recent research has explored the development of decision support systems that (i) assist human crime investigators by proposing plausible crime scenarios explaining given evidence, and (ii) provide the means to analyse such scenarios. While such approaches can generate useful explanations, they are inevitably restricted by the limitations of formal abductive inference mechanisms. Building on work presented previously at this venue, this paper characterises an important class of scenarios, containing “alternative suspects” or “hidden objects”, which cannot be synthesised robustly using conventional abductive inference mechanisms. The work is then extended further by proposing a novel inference mechanism that enables the generation of such scenarios.