We propose a peaking-free low-power high-gain observer that preserves the main feature of standard high-gain observers in terms of arbitrarily fast convergence to zero of the estimation error, while overtaking their main drawbacks, namely the "peaking phenomenon" during the transient and the numerical implementation issue deriving from the high-gain parameter that is powered up to the order of the system. Moreover, the new observer is proved to have superior features in terms of sensitivity of the estimation error to high-frequency measurement noise when compared with standard high-gain observers. The proposed observer structure has a high-gain parameter that is powered just up to two regardless the dimension of the observed system and adopts saturations to prevent the peaking of the estimates during the transient. As for the classical solution, the new observer is robust with respect to uncertainties in the observed system dynamics in the sense that practical estimation in the high-gain parameter can be proved. (C) 2018 Published by Elsevier Ltd.