In transtensional and transpressional deformation zones, bulk 3D strains are often kinematically partitioned into regions of wrench- and extension- or shortening-dominated faulting. Most strain models assume ideal incompressible materials with a Poisson's ratio (ν) of 0.5. It is well known from experimental and geophysical data, however, that natural rocks have values of ν <0.5 and that significant variations in the values of ν occur for different lithologies. We demonstrate that for non-coaxial, 3D transtension and transpression, this should lead to an expansion of the wrench-dominated strain field. The effect is especially marked in lithologies with very low Poisson's ratios (ν ≤0.15), where wrench-dominated deformation can occur even where the regional direction of divergence or convergence is only modestly oblique (e.g. 52°). The Carboniferous basin-bounding 90-Fathom Fault, NE England, was reactivated as a dextral transtensional structure during NE–SW regional stretching in post-Carboniferous times. Preferential dip-slip reactivation of pre-existing east–west structures in the underlying Carboniferous basement led to kinematic partitioning of the transtensional bulk strain. In addition, the geometric, spatial and kinematic patterns of minor faulting in Permian rocks located in the fault hanging wall are markedly influenced by the host lithology. Quartz-rich sandstones (ν=0.12) preserve complex faulting patterns consistent with a wrench-dominated transtension whereas immediately overlying dolostones (ν=0.29) preserve simpler patterns of Andersonian conjugate faults consistent with a more extension-dominated regime. We propose that the markedly different strain response during the same deformation reflects pronounced lithologically controlled variations in the value of Poisson's ratio in the adjacent rock units. Our findings illustrate that micro- to meso-scale faulting patterns are likely to be substantially influenced by lithology in all regions of oblique divergence or convergence.