We present the analysis of the deformation in the axial valley of two contrasted regions of the very slow spreading Southwest Indian Ridge based on side-scan sonar images. Our objective is to investigate how the obliquity is accommodated along the system. We show that the robust magmatic segments have axial valleys and major faults subperpendicular to spreading. The other sections show fault populations with various degrees of obliquity, often arranged in left-stepping echelons, accommodating part of the strike-slip deformation. Side-scan sonar reveals the presence of a corrugated surface near 59 degrees E interpreted to be an incipient detachment fault. We show that the large width of the SWIR oblique sections, and the difference in tectonic style between the robust volcanic segments and the magma-starved sections, is accounted for by large variations in the thickness of the brittle lithosphere. We suggest that the emplacement of mantle rocks in the surveyed amagmatic ridge sections can occur by alternating conjugate faults. Serpentinization of outcropping peridotites might also play a significant role in the development of faults in thin crust regions and the distribution of deformation in space and time.