Multi-modality positron emission tomography and computed tomography (PET-CT) imaging depicts biological and physiological functions (from PET) within a higher resolution anatomical reference frame (from CT). The need to efficiently assimilate the information from these co-aligned volumes simultaneously has resulted in 3D visualisation methods that depict e.g., slice of interest (SOI) from PET combined with direct volume rendering (DVR) of CT. However because DVR renders the whole volume, regions of interests (ROIs) such as tumours that are embedded within the volume may be occluded from view. Volume clipping is typically used to remove occluding structures by `cutting away' parts of the volume; this involves tedious trail-and-error tweaking of the clipping attempts until a satisfied visualisation is made, thus restricting its application. Hence, we propose a new automated opacity-driven volume clipping method for PET-CT using DVR-SOI visualisation. Our method dynamically calculates the volume clipping depth by considering the opacity information of the CT voxels in front of the PET SOI, thereby ensuring that only the relevant anatomical information from the CT is visualised while not impairing the visibility of the PET SOI. We outline the improvements of our method when compared to conventional 2D and traditional DVR-SOI visualisations.