A comprehensive exploration of the inverse trans-influence (ITI) phenomenon in a series of cis-[U-VI(O)(L)Cl-4](0/-) and trans[U-VI(O)(L)Cl-4](0/-) complexes involving a wide variety of neutral and anionic unidentate ligands L, using relativistic density functional theory, threw light on the still-intriguing physics of ITI, elucidated its origin, and deployed the ligands L in cis- and trans-ITI sequences (ladders). ITI is produced for the complete set of L in both series of [U(O)(L)Cl-4](0/-) complexes, but this is not reflected in the thermodynamic stability of the [U(O)(L)Cl-4](0/-) isomers. In effect the hard and strong s-donor anionic ligands stabilize the trans isomers, but the opposite is true for the soft sigma-donor/pi-donor neutral and anionic ligands that stabilize the cis isomers. According to the ITI%(U-L) metrics the hard strong sigma-donor anionic ligands exert stronger ITI than the soft sigma-donor/pi-donor neutral ones, while according to the ITI%(U-O) metrics ITI is produced only for the more stable trans-[U(O)(L)Cl-4](0/-) isomers involving the anionic ligands. In contrast the neutral ligands in the more stable cis[U(O)(L)Cl-4](0/-) isomers produce the normal cis influence (CI). Furthermore, the more electronegative ligands produce stronger ITI. ITI%(U-O) cis- and trans-philicity ladders are also built for both series of complexes employing the isotropic sigma(iso)(SO) O-17 NMR shielding constants as a sensitive metric of the ITI phenomenon. The NMR ITI%(U-O) metrics are consistent with the ITI %(U-O) ones illustrating that the isotropic O-17 NMR shifts are sensitive metrics of the covalency of the multiple U-O bonding mode and, hence, of the ITI phenomenon. Interestingly the 2 sigma BD(U-O) natural bond orbitals play a key role in tuning the bond length and covalency of the U-O bond through the 2 sigma(U equivalent to O)-> 2 sigma*(U equivalent to O) hyperconjugative interactions. The assessment of the magnitude of the ITI in the [UVI(O)(L)Cl-4](0/-) complexes and the recognition of the factors affecting ITI dispose a guide to experimentalists working in the area of uranium chemistry to develop strategies for stabilizing uranium-ligand linkages.