Practically, the attitude control of rigid bodies necessitates the estimation of the orientation and the measurement of the angular velocity. Consequently, the computational cost of the control loop is relatively high. In the present paper, two bounded control laws for attitude stabilization are proposed; the first one is designed without attitude estimation but using angular velocities measurements while the second control law does not even need angular velocity measurement. Based on saturation functions, the control laws are highly simple. Only the measurements of at least two non-collinear directional sensors are needed, which makes this new strategy suitable for embedded implementations. Moreover, the control laws are bounded, preventing the saturation of actuators and increasing their efficiency. The global convergence of the control law is proved. Simulations with some robustness tests (sensors noise and external disturbances) are performed.