A MEMS device having a movable plate supported on a substrate by a support structure that is hidden under the plate and yet which can be implemented to enable rotation of the plate with respect to the substrate about a rotation axis lying at the plate surface. As a result, the support structure does not take up any area within the plane of the plate, while enabling rotation of the plate, during which the plate does not substantially move sideways. The latter property reduces potential physical interference between neighboring plates in an arrayed MEMS device and enables implementation of a segmented mirror having relatively narrow gaps between adjacent segments and, thus, a relatively large fill factor, e.g., at least 98%.