Two different groups (Cao et al. (2015) and Sundholm et al. (2016)) have recently reported (a) experimental Nuclear Magnetic Reso-nance data and ab initio Nucleus Independent Chemical Shift (NICS) calculations, and (b) GIMIC (Gauge Including Magnetically Induced Cur-rents) ab initio computations, on the magnetic properties of some derivatives of [4n+2]-π-electron conjugated systems called 'bispentalenes'. These are formed by annellating two pentalene groups with a benzene or a naphthalene moiety. The same structures are here subjected to calculations based on the simple, pseudo graph-theoretical, Hückel-London-Pople-McWeeny (HLPM) 'topological' ring-current approach. In addition, HLPM calculations are presented on some structures with [4n]-perimeters that were also studied by Cao et al., as well as some other related, specially 'designed', [4n]- and [4n+2]-perimeter structures of our own choosing. The aim is to see whether there is qualitative, or even semi-quantitative, agreement between a (presumably) numerically accurate but necessarily complex ab initio calculation and a conceptually simple, quasi graph-theoretical one - the HLPM approach - whose predictions depend only on the carbon-carbon connectivity of the struc-ture being investigated, and on the (geometrical) areas of its individual constituent rings. The HLPM calculations agree with the more-sophis-ticated studies that all the structures examined, whether they be [4n]- or [4n+2]-perimeter systems, bear paramagnetic π-electron currents around their perimeters. Furthermore, all the many pentalene moieties in these conjugated systems appear to undergo incorporation into these bispentalene structures with - to greater or lesser extents - their characteristic perimeter circulations in the paramagnetic sense sur-viving intact. Quantitative regression comparisons between GIMIC ab initio integrated bond-current susceptibilities and HLPM bond-current intensities in a small sample of bonds in the structures studied by Sundholm et al. are found to have a correlation coefficient of 0.94 - not as high as that obtained (0.98) when similar data for a larger sample of bonds in several alternant, condensed, benzenoid were previously com-pared. It is again emphasised that Pople and Untch's rule about [4n+2]-annulenes being diamagnetic and [4n]-ones being paramagnetic - like the famous Hückel Rule itself - rigorously applies only to monocycles.