Thermal models based on the geometry of axial segmentation, and mechanical models of axial valley formation, suggest that the axial lithosphere of slow spreading ridges can be thicker than the crust modeled from gravity data, or measured from seismic data. This is particularly the case in thin crust ridge regions that are near axial discontinuities. The temperature field modeled in these thin crust ridge regions is such that some of the melts extracted from the asthenosphere should crystallize in the mantle, before they reach the crust. This prediction is consistent with observations made on gabbroic and ultramafic samples collected in thick lithosphere/thin crust regions of the Mid-Atlantic Ridge, and along the ultra-slow Southwest Indian Ridge. A geological model is proposed for the lithosphere created in these thick lithosphere/thin crust ridge regions. This model suggests that crustal thicknesses measured in seismic surveys of these regions do not directly reflect the melt production in the asthenosphere beneath the ridge: some of the melt gets trapped in the mantle, and part of the crust is made of variably fractured and serpentinized residual ultramafics. Potential consequences on the way we interpret along-axis crustal thickness variations at slow spreading ridges are discussed and evaluated.