Zenithal openings are attractive because they provide a high illuminance level. Nevertheless, this type of opening may create glare or overheating due to the penetration of direct sunlight. Conventional protective systems, north oriented sheds, unfortunately reduce the daylighting performance when the sky is overcast. On the other hand, movable blinds give a good compromise but introduce reliability and maintenance problems. In the present paper, a new concept of a top opening without moving parts is developed and analysed. Based on anidolic optics (non-imaging optics), this device gives efficient solar protection and reflects inside the building a large part of the diffuse natural light. In the present situation, the numerical simulations show that, in overcast conditions, this system is equivalent to horizontal glazing with a transmittance of 58%. Compared to sheds, this device increases significantly the building lighting autonomy and the visual comfort.