The corrugated form of the Harcuvar, South Mountains, and Catalina metamorphic core complexes in Arizona reflects the shape of the middle Tertiary extensional detachment fault that projects over each complex. Corrugation axes are approximately parallel to the fault-displacement direction and to the footwall mylonitic lineation. The core complexes are locally incised by enigmatic, linear drainages that parallel corrugation axes and the inferred extension direction and are especially conspicuous on the crests of antiformal corrugations. These drainages have been attributed to erosional incision on a freshly denuded, planar, inclined fault ramp followed by folding that elevated and preserved some drainages on the crests of rising antiforms. According to this hypothesis, corrugations were produced by folding after subacrial exposure of detachment-fault foot-walls. An alternative hypothesis, proposed here, is as follows. In a setting where preexisting drainages cross an active normal fault, each fault-slip event will cut each drainage into two segments separated by a freshly denuded fault ramp. The upper and lower drainage segments will remain hydraulically linked after each fault-slip event if the drainage in the hanging-wall block is incised, even if the stream is on the flank of an antiformal corrugation and there is a large component of strike-slip fault movement. Maintenance of hydraulic linkage during sequential fault-slip events will guide the lengthening stream down the fault ramp as the ramp is uncovered, and stream incision will form a progressively lengthening, extension-parallel, linear drainage segment. This mechanism for linear drainage genesis is compatible with corrugations as original irregularities of the detachment fault, and does not require folding after early to middle Miocene footwall exhumations. This is desirable because many drainages are incised into nonmylonitic crystalline footwall rocks that were probably not folded under low-temperature, surface conditions. An alternative hypothesis, that drainages were localized by small fault grooves as footwalls were uncovered, is not supported by analysis of a down-plunge fault projection for the southern Rincon Mountains that shows a linear drainage aligned with the crest of a small antiformal groove on the detachment fault, but this process could have been effective elsewhere. Lineation-parallel drainages now plunge gently southwestward on the southwest ends of antiformal corrugations in the South and Buckskin Mountains, but these drainages must have originally plunged northeastward if they formed by either of the two alternative processes proposed here. Footwall exhumation and incision by northeast-flowing streams was apparently followed by core-complex arching and drainage reversal.