Following the success of the first mission, the High-Resolution Coronal Imager (Hi-C) was launched for a third time (Hi-C 2.1) on 2018 May 29 from the White Sands Missile Range, NM, USA. On this occasion, 329 s of 17.2 nm data of target active region AR 12712 were captured with a cadence of ≈4 s, and a plate scale of 0.″129 pixel-1. Using data captured by Hi-C 2.1 and co-aligned observations from SDO/AIA 17.1 nm, we investigate the widths of 49 coronal strands. We search for evidence of substructure within the strands that is not detected by AIA, and further consider whether these strands are fully resolved by Hi-C 2.1. With the aid of multi-scale Gaussian normalization, strands from a region of low emission that can only be visualized against the contrast of the darker, underlying moss are studied. A comparison is made between these low-emission strands and those from regions of higher emission within the target active region. It is found that Hi-C 2.1 can resolve individual strands as small as ≈202 km, though the more typical strand widths seen are ≈513 km. For coronal strands within the region of low emission, the most likely width is significantly narrower than the high-emission strands at ≈388 km. This places the low-emission coronal strands beneath the resolving capabilities of SDO/AIA, highlighting the need for a permanent solar observatory with the resolving power of Hi-C.