In generally well-connected high-temperature superconducting strands the overall measured transport critical current density (CCD), J cT,meas (`averaged' over grains and grain boundaries) is suppressed (or `throttled') to less than its maximum possible value, here referred to as the intrinsic CCD, J cT,intr, as a result, for example, of filament-diameter undulations (sausaging), path constrictions due to non-superconducting inclusions, cracking, and in extreme cases filament breakage. A realizable goal in the form of an estimated J cT,intr is a valuable adjunct to process optimization activities. It is shown that in fine-filament monocore or multifilamentary (MF) strands the magnetically measured CCD, J c,mag, although not necessarily equal to J cT,intr provides a useful lower limit to it. By the same token, in bridged MF strands the saturated bridged magnetization, Δ M br,sat, under ideal conditions could yield an actual value for J cT,intr, and in general will provide a lower limit. Based on these principles, analysis of the bridged magnetizations of a group of round MF Bi:2212/Ag strands yielded J ct,intr (4.2 K) lower limits of 3∼7×10 5 A/cm 2.