Gas permeability data are presented for mixed matrix membranes (MMMs) of few-layer graphene in the polymer of intrinsic microporosity PIM-1, and the results compared with previously reported data for two other nanofillers in PIM-1: multiwalled carbon nanotubes functionalized with poly(ethylene glycol) (f-MWCNTs) and fused silica. For few-layer graphene, a significant enhancement in permeability is observed at very low graphene content (0.05 vol.%), which may be attributed to the effect of the nanofiller on the packing of the polymer chains. At higher graphene content permeability decreases, as expected for the addition of an impermeable filler. Other nanofillers, reported in the literature, also give rise to enhancements in permeability, but at substantially higher loadings, the highest measured permeabilities being at 1 vol.% for f-MWCNTs and 24 vol.% for fused silica. These results are consistent with the hypothesis that packing of the polymer chains is influenced by the curvature of the nanofiller surface at the nanoscale, with an increasingly pronounced effect on moving from a more-or-less spherical nanoparticle morphology (fused silica) to a cylindrical morphology (f-MWCNT) to a planar morphology (graphene). While the permeability of a high-free-volume polymer such as PIM-1 decreases over time through physical ageing, for the PIM-1/graphene MMMs a significant permeability enhancement was retained after eight months storage.