The conditions under which continental rifting may occur without an accompanying protracted period of synextensional magmatism are explored with a series of finite element models that dynamically simulate continental extension. The models demonstrate that 5–7 km of new oceanic crust can be generated at the time of breakup while restricting synextensional magmatism to less than 2 m.y. prior to the end of the rifting episode if the extension rate exceeds ∼15 mm/yr and the crust contains only minor lateral variations in strength. Under these conditions, extensional strain in the mantle is localized during the early stages of rifting, preventing diffuse lithospheric thinning. Melting does not begin until lithospheric necking is well established, resulting in a narrow zone of melt production that limits magmatism to within ∼30 km of the ocean-continent boundary. Once melting begins, rifting progresses rapidly to breakup, restricting the period of synextensional magmatism to as little as 1.6 m.y. prior to the onset of sea-floor spreading. Because the models do not require either a cool mantle prior to rifting or pronounced conductive cooling of the mantle during rifting, they are able to account for the generation of new oceanic crust at the time of breakup. The model predictions are consistent with the structure and magmatic history of nonvolcanic rifted margins in the North Atlantic Ocean.