The Asal-Ghoubbet Rift (AG Rift) in Djibouti lies in the subaerial continuation of the Aden ridge system, thereby constituting a unique location to study rifting processes and mechanisms involved in continental breakup and oceanic spreading. Continually upgraded and expanded geodetic technology has been used to record the 1978 Asal rifting event and postdiking deformation. In light of recent results obtained for the Manda Hararo-Dabbahu rifting event (2005–2010), we propose that the horizontal and vertical geodetic data can be modeled with a double source, involving a dike-like inflation component aligned along the rift axis and a spherical pressure source located at midsegment below the Fieale caldera. By revisiting the codiking data, we propose that the reservoir below Fieale could have fed, at least partially, the 1978 injection and the contemporaneous Ardoukôba eruption and potentially induced local subsidence due to magma draining out of the central reservoir. As an alternative to previously proposed viscoelastic relaxation models, we reinterpret postdiking observations using a purely elastic rheology. We determine the relative contribution of a midsegment reservoir inflation and a dike-like opening component, together with their respective time evolutions. Our results suggest that interactions between steadily accumulating tectonic strain and temporal variations in melt supply to the shallow magma plumbing system below the AG Rift may entirely explain the geodetic observations and that viscoelastic deformation processes played a minor role in the 30 years following the 1978 rifting event.