The polarization pattern of the sky is exploited by many insects for spatial orientation and navigation. It derives from Rayleigh scattering in the atmosphere and depends directly on the position of the sun. In the insect brain, the central complex (CX) houses neurons tuned to the angle of polarization (AoP), that together constitute an internal compass for celestial navigation. Polarized light is not only characterized by the AoP, but also by the degree of polarization (DoP), which can be highly variable, depending on sky conditions. Under a clear sky, the DoP of polarized sky light may reach up to 0.75 but is usually much lower especially when light is scattered by clouds or haze. To investigate how the polarization-processing network of the CX copes with low DoPs, we recorded intracellularly from neurons of the locust CX at different stages of processing, while stimulating with light of different DoPs. Significant responses to polarized light occurred down to DoPs of 0.05 indicating reliable coding of the AoP even at unfavorable sky conditions. Moreover, we found that the activity of neurons at the CX input stage may be strongly influenced by nearly unpolarized light, while the activity of downstream neurons appears less affected.