Others have explained the excess flattening of Iapetus by a model in which the moon formed at a high spin rate, achieved isostatic equilibrium by very rapid interior heating caused by short-lived radioactive isotopes (SLRI), and subsequently cooled, locking in the excess flattening with respect to an equilibrium shape at its present spin rate. Here we propose an alternate model that does not require an unusually high initial spin rate or the SLRI. The initial formation of Iapetus results in a slightly oblate spheroid with porosity >10%. Radioactive heating by long-lived isotopes warms the interior to about 200 K, at which point it becomes ductile and the interior compacts by 10%, while the 120 km-thick exterior shell remains strong. The shell must deform to match the reduced volume of the ductile interior, and we propose that this deformation occurs along the equator, perhaps focused by a thinner equatorial shell. The final shape of the collapsed sphere matches the observed shape of Iapetus today, described as an oblate ellipse, except along the equator where strain concentration forms a broad ridge. To maintain this non-equilibrium shape, the thickness of the shell must exceed 120 km. Testing the equatorial focusing hypothesis will require a model that includes non-linear processes to account for the finite yield strength of the thick lithosphere. Nevertheless, we show that the stress in the lithosphere generated by the contraction of the interior is about 3 times greater than the stress needed to deform the lithosphere, so some type of lithospheric deformation is expected.