So far, studies that investigated interference effects of post-learning processes on episodic memory consolidation in humans have used tasks involving only complex and meaningful information. Such tasks require reallocation of general or encoding-specific resources away from consolidation-relevant activities. The possibility that interference can be elicited using a task that heavily taxes our limited brain resources, but has low semantic and hippocampal related long-term memory processing demands, has never been tested. We address this question by investigating whether consolidation could persist in parallel with an active, encoding-irrelevant, minimally semantic task, regardless of its high resource demands for cognitive processing. We distinguish the impact of such a task on consolidation based on whether it engages resources that are: (1) general/executive, or (2) specific/overlapping with the encoding modality. Our experiments compared subsequent memory performance across two post-encoding consolidation periods: quiet wakeful rest and a cognitively demanding n-Back task. Across six different experiments (total N = 176), we carefully manipulated the design of the n-Back task to target general or specific resources engaged in the ongoing consolidation process. In contrast to previous studies that employed interference tasks involving conceptual stimuli and complex processing demands, we did not find any differences between n-Back and rest conditions on memory performance at delayed test, using both recall and recognition tests. Our results indicate that: (1) quiet, wakeful rest is not a necessary prerequisite for episodic memory consolidation; and (2) post-encoding cognitive engagement does not interfere with memory consolidation when task-performance has minimal semantic and hippocampally-based episodic memory processing demands. We discuss our findings with reference to resource and reactivation-led interference theories