Magmatic accretion at slow-spreading mid-ocean ridges exhibits specific features. Although magma supply is focused at the centre of second-order segments, melts are episodically distributed along the rift toward segment ends by lateral dyke intrusions. It has been previously suggested that an along-axis downward topographic slope away from the magma source is sufficient to explain lateral dyke propagation. However, this cannot account for the poor correlation between dyke opening and surface elevation in the 2005-2010 series of 14 dyke intrusions of Afar (Ethiopia). Using mechanical arguments, constrained by both geodetic and seismological observations, we propose that the large dykes that initiate near the mid-segment magma source are attracted toward segment ends as a result of a thickening of the elastic-brittle lithosphere in the along-rift direction. This attraction arises from the difference of elastic resistance between the segment centre where the lithosphere is thermally weakened by long-term focusing of melts, and comparatively "colder", hence stronger segment ends. The axial topographic gradient in magmatic rifts may be more likely explained as an incidental consequence of these variations of along-axis elastic-brittle thickness, rather than the primary cause of lateral dyke injections.