THE recent discoveries of superconductivity at 94 K in the single-CuO2-layer compound HgBa2CuO4+x (Hg-1201)1 and at 133 K in its two- and three-copper-layer analogues 2(Hg-1212 and Hg-1223) have renewed interest in the search for new high-transition-temperature (high-T(c)) superconductors. But whatever the T(c), high values of intergrain critical current density are required for large-scale applications; thus, the material must have good electromagnetic connectivity between grains (it must not be electromagnetically granular) and it should be able to maintain its current-carrying capacity in high magnetic fields (it should have a high irreversibility field, H*(T)). Putilin et al.1 surmised that the small CuO2 layer spacing of Hg-1201 might yield a high H*(T). We report here that H*(T) is indeed significantly higher than for the two- and three-copper-layer Bi-Sr-Ca-Cu-O compounds (Bi-2212 and Bi-2223), but lower than for YBa2Cu3O7 (Y-123). The low-temperature flux pinning is also strong. Like Y-123, however, Hg-1201 is electromagnetically granular. A high degree of grain alignment will probably be necessary to remove this granularity; by analogy with the bismuth compounds, this is likely to be easier if the two-mercury-layer counterparts of Bi-22XY (Hg-2201, -2212 or -2223) can be synthesized.