We present the first model results showing that some core complex detachment faults are strong and that their strength has to be in a narrow range to allow certain extensional structures to develop. The structures we simulate are kilometer-scale “rider blocks” that are particularly well observed on some oceanic core complexes as well as continental metamorphic core complexes. Previous numerical simulations of lithospheric extension produced the large-offset, core complex-forming, normal faults only when the faults were weaker than a given threshold. However, our new, high-resolution simulations indicate that rider blocks only result when the faults are stronger than a given level. A narrow range of fault weakening, relative to intact surrounding rock, allows for a consecutive series of rider blocks to emerge in a core complex-like geometry. Our results show that rider blocks develop when the dominant form of weakening is by reduction of fault cohesion while faults that weaken primarily by friction reduction do not form distinct rider blocks.