Profiles through the summit of a small nearly axisymmetric extrusion of Oligocene and Miocene salt, and simple analogue models of it, simulate the profiles of piles of ductile nappes extruded from convergent orogens. The salt extrudes from a reactive diapir along a major strike-slip fault at about 82 mm a−1 and rises 315 m above the central plateau of Iran. The salt has the distinctive smooth profile of a viscous fountain in which an asymmetric apron of allochthonous salt gravity-spreads over its surroundings from a summit dome. Curtain folds developed in the source layer extrude from the diapir and are refolded by major recumbent folds with circumferential axes that simulate nappes. Minor flow folds with circumferential axes refold major folds in the top 10-50 m of surficial salt. Master joints >100 m long indicate brittle failure of dilated salt by regional stress fields. Tuned to the dimensions of Qum Kuh, analytical and analogue models of viscous extrusions constrain the dynamic salt budget and a time of extrusion of at least 42 000 years. New analogue models suggest that the number, amplitude and spacing of major recumbent folds within the extruded salt (and ductile nappe piles) record the number, amount and relative timing of fluctuations in the driving forces.