The search for rocky exoplanets plays an important role in our quest for extra-terrestrial life. Here, we discuss the extreme physical properties possible for the first characterised rocky super-Earth, CoRoT-7b ( R pl = 1.58 ± 0.10 R Earth, M pl = 6.9 ± 1.2 M Earth). It is extremely close to its star ( a = 0.0171 AU = 4.48 R st), with its spin and orbital rotation likely synchronised. The comparison of its location in the ( M pl, R pl) plane with the predictions of planetary models for different compositions points to an Earth-like composition, even if the error bars of the measured quantities and the partial degeneracy of the models prevent a definitive conclusion. The proximity to its star provides an additional constraint on the model. It implies a high extreme-UV flux and particle wind, and the corresponding efficient erosion of the planetary atmosphere especially for volatile species including water. Consequently, we make the working hypothesis that the planet is rocky with no volatiles in its atmosphere, and derive the physical properties that result. As a consequence, the atmosphere is made of rocky vapours with a very low pressure ( P ⩽ 1.5 Pa), no cloud can be sustained, and no thermalisation of the planet is expected. The dayside is very hot (2474 ± 71 K at the sub-stellar point) while the nightside is very cold (50-75 K). The sub-stellar point is as hot as the tungsten filament of an incandescent bulb, resulting in the melting and distillation of silicate rocks and the formation of a lava ocean. These possible features of CoRoT-7b could be common to many small and hot planets, including the recently discovered Kepler-10b. They define a new class of objects that we propose to name " Lava-ocean planets".