The Carboniferous Billefjorden rift basin is a well-known example of a suite of Carboniferous basins on the Barents Shelf and NE Greenland. The basin has a clastic, carbonate and evaporite fill with complex and disputed stratigraphic relationships, especially regarding the Ebbadalen and Minkinfjellet formations. Geometrically, the basin is considered a simple half-graben. A N–S-trending fault and monocline structure within the northern portion of the basin, the Løvehovden fault, has lithological and thickness differences across it within the Minkinfjellet and possibly Ebbadalen formations. The fault shows W-side-down movement, defining a sub-basin within the larger half-graben. Significant along-strike changes occur. Down-throw to the west is at least 150 metres and possibly 400 metres, as shown by across-fault thickness differences of Ebbadalen and/or Minkinfjellet formations. To the east of the fault, the contact between the Ebbadalen and Minkinfjellet formations is a disconformity with significant local relief, and is interpreted to represent exposure from footwall uplift, and associated near- or at-surface solution, producing basal stratiform breccias. A similar contact is not exposed west of the fault. Monoclinal deformation and thickening of the younger Wordiekammen Formation above and across the monocline constrain a later movement component. Kinematic data and the structural style clearly indicate the Løvehovden fault is a normal fault with associated tri-shear zone development, consistent with the regional Carboniferous rift setting. Earlier interpretations describe the Løvehovden fault and monocline as Tertiary contractional features. In contrast, our work advocates that they are an important architectural basin element, defining a sub-basin within the Billeforden Trough during Minkinfjellet Formation deposition, with insignificant, if any, Tertiary reactivation. The Løvehovden fault is aligned with and represents the southern termination of the Lemströmfjellet fault to the north. Thus, the Billefjorden basin changes from a narrow graben to a broader half-graben to the south. These along-strike changes have important implications for the stratigraphic architecture of the basin, and for palaeogeographic reconstructions. These results and application of 3-D models for extension related tri-shear zones may help inform interpretation of other Carboniferous basins on the Barents Shelf.