The Southwest Indian Ridge is a slow spreading end-member of the mid-ocean ridge system. The deepest borehole penetrating the lower oceanic crust, Ocean Drilling Program hole 735B, lies on the eastern transverse ridge of the Atlantis II Fracture Zone at 57 ¿E. A wide-angle seismic survey in the vicinity of the borehole reveals a crustal structure that is highly heterogeneous. To the east of Atlantis Bank, on which hole 735B is located, the crust consists of a 2--2.5 km thick high-velocity-gradient oceanic layer 2 and a 1--2 km thick low-velocity-gradient layer 3. The transform valley has a 2.5--3 km thick crust with anomalously low velocities interpreted to consist largely of highly serpentinized mantle rocks. The seismically defined crust is thickest beneath the borehole, where layer 2 is thinner and the lower crust is inferred to contain 2--3 km of partially serpentinized mantle. The seismic velocity models are consistent with gravity data which show weak residual mantle Bouguer anomalies because the regions of thinner crust have lower crustal densities. Stress variations deduced from mass balances between the transform valley floor and the adjacent transverse ridges are much larger than the likely threshold for lithospheric failure and therefore indicate that the relief is supported dynamically. The variation of crustal thickness with spreading rate defined by data from the Southwest Indian Ridge and elsewhere is consistent with models of melt generation in which the upwelling mantle is cooled by conductive heat loss at very slow spreading rates, resulting in reduced melt generation under the spreading axis. Large segment-scale variations in crustal thickness suggest subcrustal along-axis migration of melt toward segment centers. ¿ 2001 American Geophysical Union