The Catalan Coastal Ranges mark the transition from the Iberian Massif to the active tectonic region of the western Mediterranean Sea in northeastern Spain. Seismic, gravity and thermal data indicate that the crust and lithosphere thin from the Ebro basin of the Iberian Massif to the Valencia trough of the western Mediterranean, consistent with the present elevations of these provinces. Mid-Tertiary sediment transport directions, however, indicate that the Catalan Coastal Ranges were below the elevation of the Valencia trough during the mid-Tertiary, and that an inversion of their relative topographies has occurred associated with Neogene extension in this region. A formulation of lithospheric buoyancy has been used to back-calculate possible pre-extension lithospheric structures consistent with the mid-Tertiary elevation constraints and lithospheric strength constraints. The back-calculation method allows to obtain a range of stretching factors for the crust and for the lithospheric mantle independently from each other. These calculations suggest a suite of modes of lithospheric deformation ranging from pure shear of an initially heterogeneous lithosphere to differential stretching of a homogeneous lithosphere, both with significant components of thermal modification of the lithosphere not directly associated with convection through extension. We conclude that although the basic features of basin formation may be explained by elegant simple models of lithospheric extension, the details of elevation changes associated with extension suggest a significant degree of non-uniqueness in these models.