A case for a cosmetic or body hygiene product comprises a body having a bottom and a free edge (2B) and containing a dish (5) containing a solid, pasty or pulverulent product, and a lid (3) mounted pivotably on the body. It also comprises movable equipment (11) comprising the dish and a hinge region (10) by which the lid is hinged thereto and which is able to undergo translational movement perpendicularly with respect to the bottom, and at least one elastically compressible assembly (40) having two stable withdrawn positions with respect to a maximum pushed-in position, said assembly being inserted between the body and the movable equipment so as to delimit for this equipment a maximum pushed-in configuration and a minimum pushed-in configuration, these configurations being such that, when the movable equipment is in the maximum pushed-in configuration and the lid is in the closed configuration, the hinge region of the equipment and at least part of this lid are retracted into the body whereas, when this equipment is in the minimum pushed-in position, the hinge region is at least partly outside the body so that the lid can pivot between its configurations and the lid has a sufficient handhold for a user to carry out this pivoting movement.