The formation of highly extended continental margins is much debated and it remains unclear whether these margins form by uniform or depth-dependent stretching of lithosphere. The existence and form of depth dependency at deep-water margins is of considerable importance to hydrocarbon exploration. Recent discussion has centred on the amagmatic Newfoundland-Iberia conjugate margins where dense seismic wide-angle and deep reflection surveying has yielded well-resolved images of the crust and lithospheric mantle. We have tackled the problem of depth-dependency in three steps. First, we have reconstructed water-loaded subsidence histories by making simple assumptions about changes in water depth through time. Secondly, we have used these reconstructed subsidence histories to determine the spatial and temporal variation of lithospheric strain rate. Crucially, we make no prior assumptions about the existence and form of depth dependency. Inverse modelling has yielded excellent fits to both reconstructed subsidence and crustal thickness observations. Strain rate distributions are depth-dependent, suggesting that lithospheric mantle thins over a wider region than the crust. In order to avoid generating substantial volumes of syn-rift melt, crustal strain rates greatly exceed lithospheric mantle strain rates beneath highly-extended parts of the crust. These strain rate distributions control the growth and heat flow history of the conjugate margins through space and time.