The rudimentary Huckel-London-Pople-McWeeny (HLPM) formalism, which frequently mimics the predictions of more-sophisticated ab initio approaches, is used to investigate the g-electron ring-current and bond-current properties of four novel altan-structures, the parents of three of which are conjugated structures with "fixed" single carbon carbon bonds: namely, acenaphthylene, fluoranthene, and perylene. Such structures are nowadays sometimes called "K-factorizable". Non-K-factorizable peropyrene is also considered, for comparison. The remarkably contrasting sizes of the bond-currents in the unshared bonds situated in the centers of perylene and peropyrene, first noted more than 40 years ago, are preserved in the corresponding bonds of the respective altan-structures. Current patterns in the parent structures frequently remain semiquantitatively intact when the parent is formally converted to the corresponding altan, a finding that largely agrees with the predictions of previous ab initio calculations. The circulations around the [4n]-perimeters of all four of the altans considered here are (as expected) in the clockwise (paramagnetic) direction.