Rift-basin stratigraphy commonly records an early stage of slow subsidence followed by an abrupt increase in subsidence rate. The physical basis for this transition is not well understood, although an increase in extension rate is commonly implied. Here, a numerical fault-growth model is used to investigate the influence of segment linkage on fault-displacement-rate patterns along an evolving normal fault array. The linkage process we describe is controlled by a stress feedback mechanism, which leads to enhanced growth of optimally positioned faults. Model results indicate that, even with constant extension rates, slow displacement rates prevail during an initial phase of distributed extension, followed by an increase in displacement rates as strain becomes localized on linked fault arrays. This is due to the dynamics of fault interactions rather than mechanical weakening. Comparison of model simulations with rift-basin subsidence and stratigraphic patterns in the Gulf of Suez and North Sea suggests that the occurrence and timing of rapid basin deepening can be explained by the mechanics of fault-zone evolution, without invoking a change in regional extension rates.