We describe a new model for melt generation by mantle decompression during uniform pure shear extension of continental lithosphere at finite rates. As the duration of rifting increases, conductive heat loss from the upwelling mantle causes the amount of melt generated beneath a rift to decrease. Melt generation is strongly dependent on rift duration because most melt is generated in the region near the top of the upwelling asthenosphere, where conductive cooling is greatest when the lithosphere is extended at a finite rate. Whereas instantaneous thinning of the lithosphere by a factor of 5 generates more than 2 km of melt as the underlying normal temperature mantle decompresses, rifting over a period of 15 m.y. reduces the melt generation to zero as heat is lost vertically by conduction. If the underlying mantle is initially abnormally hot, at 1400¿C or 100¿C hotter than normal, then the thickness of melt generated during a 15-m.y. period of rifting is reduced to only half of the 8.5 km produced by instantaneous stretching. Lateral heat conduction to the adjacent unextended lithosphere further reduces the mantle melting. Temporal variation in the rate of extension also affects melting. We compile results from the ''nonvolcanic'' rifted continental margins of the North Atlantic and show that they exhibit little synrift magmatism, despite extreme thinning of the continental crust. If rifting had occurred instantaneously, several kilometers thickness of melt should have been generated by such large degrees of lithospheric thinning. We show that rifting lasted typically 15--25 m.y., which from the results of our model is sufficient to suppress completely melt generation from normal potential temperature asthenosphere. The production of abnormally thin oceanic crust immediately adjacent to the rifted continental margins may also reflect significant cooling of the asthenospheric mantle during the long period of continental extension prior to breakup. ¿ American Geophysical Union 1995