Diffusion-limited, heterogeneously-catalysed processes mean choices influencing pore structure-transport relationships, made during pellet fabrication, affect product performance. This work shows how the ‘sifting strategy’ can identify the critical aspects of a highly complex catalyst pellet pore structure that control mass transport to construct an idiosyncratic, minimalist model. This is implemented using fully-integrated gas overcondensation, mercury porosimetry and X-ray tomography experiments. It showed high temperature shift (HTS) catalyst pellets had a trimodal pore structure. The second mode, consisting of macropores within the roll-compacted feed particles, controlled mass transport. Knudsen-regime mass transport was shown to be critically-controlled by an incipiently-percolating cluster of these intermediate-sized macropores, as its rate could be drastically reduced via introduction of very few blockages via mercury entrapment. This incipiently percolating network could be represented by a lattice-based, random cluster model. X-ray tomographic images, analysed with an AI segmentation algorithm, validated the proposed model of interpretation for the indirect characterization data.