Electrically tunable lenses are conceived as deformable adaptive optical components able to change focus without motor-controlled translations of stiff lenses. In order to achieve large tuning ranges, large deformations are needed. This requires new technologies for the actuation of highly stretchable lenses. This paper presents a configuration to obtain compact tunable lenses entirely made of soft solid matter (elastomers). This was achieved by combining the advantages of dielectric elastomer actuation (DEA) with a design inspired by the accommodation of reptiles and birds. An annular DEA was used to radially deform a central solid-body lens. Using an acrylic elastomer membrane, a silicone lens and a simple fabrication method, we assembled a tunable lens capable of focal length variations up to 55%, driven by an actuator four times larger than the lens. As compared to DEA-based liquid lenses, the novel architecture halves the required driving voltages, simplifies the fabrication process and allows for a higher versatility in design. These new lenses might find application in systems requiring large variations of focus with low power consumption, silent operation, low weight, shock tolerance, minimized axial encumbrance and minimized changes of performance against vibrations and variations in temperature.