We present a novel smart visibility system for visualizing crowded volumetric data containing many object instances. The presented approach allows users to form groups of objects through membership predicates and to individually control the visibility of the instances in each group. Unlike previous smart visibility approaches, our approach controls the visibility on a per-instance basis and decides which instances are displayed or hidden based on the membership predicates and the current view. Thus, cluttered and dense volumes that are notoriously difficult to explore effectively are automatically sparsified so that the essential information is extracted and presented to the user. The proposed system is generic and can be easily integrated into existing volume rendering applications and applied to many different domains. We demonstrate the use of the volume conductor for visualizing fiber-reinforced polymers and intracellular organelle structures.