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Central Tunisia has been subjected to a complex series of successive regional tectonic phases, both extensional and compressional. This history is made even more complex by the presence of mobile Triassic evaporites that generated halokinetic deformation and partly decoupled the subsalt "basement" from the overburden. At the southern end of a major regional lineament called "the North-South Axis" are some enigmatic structures (described as "Perched Synclines" in the literature) cored by the Upper Eocene Jebs Formations: the Kef En Nsour and Zebbeus structures. The core of these structures is made of synform (concave-upward) strata of Upper Cretaceous to Cenozoic age resting unconformably onto the Triassic evaporites. A significant part of the stratigraphic series (i.e., Lower Cretaceous) is missing. The Cenozoic strata are particularly thick within the synclines, whereas they are thin or absent outside the synclines. These form topographic highs raised above the regional datum. In contrast, the Mesozoic series is continuous and thicker outside the synclines. We hypothesize that these so-called "perched synclines" have a halokinetic, rather than a solely tectonic origin. The absence of parts of the lower stratigraphic series in the center of the structure indicates that the Triassic evaporites were rising as a passive diapir. During the Cenozoic, source-layer depletion combined with local extension forced the diapir to fall and its crest to subside, thus trapping thicker overburden strata within the syncline and bending them, resulting in a concave-upward geometry. During the latest stage a phase of N–S regional shortening rejuvenated the fallen diapir, raising its synform roof above the regional datum. We provide field and geophysical data, as well as results from a set of analogue models to test and validate such a Rise-Fall-Rise structural history. The final geometry changes when varying the amounts and rates of passive diapir rise, sedimentation, extension, and late shortening. Results from most experiments closely match the geometries of the field examples from Central Tunisia. In addition, one model, in which the amount of diapir fall (and extrusion) was extreme, is very similar to the Tunb Diapir located offshore SW Iran. [Display omitted] • We hypothesize a halokinetic and a tectonic origin of the perched synclines in central Tunisia. • We use geological cross sections, field observations and a gravimetric map as well as analogue modelling. • We demonstrate a Rise-Fall-Rise diapiric history. • The final geometry changes when varying the amounts and rates of passive rise, sedimentation, extension and late shortening. [ABSTRACT FROM AUTHOR]