Dark current is shown to be significantly reduced in quantum well infrared photodetectors in the tunneling regime, i.e., at very low temperature, by shifting the dopant impurity layers away from the central part of the wells. This result confirms that the interwell tunneling current is dominated by charged impurity scattering in usual structures. The experimental results are in good quantitative agreement with the proposed theory. This dark current reduction is pushing further the ultimate performances of quantum well infrared photodetectors for the detection of low infrared photon fluxes. Routes to further improvements are briefly sketched.