‘Inversion structures’ (e.g. folds, reverse faults) spatially associated with basin-bounding faults are very widely recognised in rift basins in both onshore and offshore settings worldwide. The great majority of such structures are attributed to local or regional crustal shortening events. There is, however, an alternative, which is investigated in this paper: inversion could reflect a horizontal shortening component of deformation formed during progressive and partitioned transtension. A case study from the Carboniferous Northumberland Basin shows that shortening structures can also form in obliquely divergent rifts if the bulk strain undergoes kinematic partitioning into distinct regions of wrench- and extension-dominated transtension. Such strain partitioning appears to be particularly favoured in basins where fault localisation is strongly influenced by pre-existing basement structures. This may occur because the pre-existing anisotropies are zones of long-lived weakness that lie in an orientation particularly favourable to the preferential accommodation of either strike-slip or dip-slip displacements. Our strain analysis applied to the Northumberland Basin, traditionally considered as a classic example of a Variscan inverted basin, reduces the deformation history to a single kinematically partitioned phase of dextral transtension during the late Carboniferous–early Permian. Our findings have profound implications for the interpretation of inversion structures in any rift basin where the direction of extension may be significantly oblique to the basin margins.