We propose a new type of Wave Front Sensor (WFS) derived from the Pyramid WFS (PWFS). This new WFS,called the Flattened Pyramid-WFS (FPWFS), has a reduced Pyramid angle in order to optically overlap the fourpupil images into an unique intensity. This map is then used to derive the phase information. In this paper thisnew WFS is compared to two existing WFSs, namely the PWFS and the Modulated PWFS (MPWFS) followingtests about sensitivity, linearity range and low photon flux behavior. The FPWFS turns out to be more linearthan a modulated pyramid for the high-spatial order aberrations but it provides an improved sensitivity comparedto the non-modulated pyramid. Furthermore, the pixel arrangement being more efficient than for the PWFS,the FPWFS seems particularly well suited for high-contrast applications. A first quick study of the influenceof the angle of the pyramid shows that, it is possible, with a quite constant linear range, to adjust the spatialfrequencies range where the sensitivity is the best. Finally, we also show that replacing the pyramid with aflattened cone also leads to very promising noise propagation properties.