Besides the intrinsic rheological layering of the lithosphere and its thermal structure, inherited heterogeneities may play an important role in strain localization during continental extension. This is similar to the role that defects play in the failure and necking of other materials. Here, we consider both inherited small-scale weak zones and the effects of lateral juxtaposition of two lithospheres with differing properties as mechanisms to localize deformation and initiate necking instabilities. Using 2D finite-element models that contain lateral lithospheric boundaries, in combination with smaller scale heterogeneities, we illustrate that two controls determine how necking instabilities grow and thus lead to varying styles of rifting: Control 1, the stiff/pliable nature of the lithosphere and Control 2, the background strain rate in the lithosphere. Control 1 depends on the lithospheric rheology, such that necking instabilities grow faster in materials with high power-law creeping flow exponents (stiff, brittle lithosphere) than in those with low power-law creeping flow exponents (pliable, viscous lithosphere). Control 2 prevails in lithosphere where background strain rates are highest. This happens because necking amplifies the background strain rate in power-law materials, leading to faster necking where strain rates are highest. The model results show that Control 2 determines the location of localization, unless the background strain rate is equal or near equal in both lithospheres, in which case Control 1 wins. These results explain why rifting does not localize in cratons even though they contain heterogeneities. The results also provide a mechanism for the formation of asymmetric rifted margins.