In this work we focus on speaker verification on channels of varying quality, namely Skype and high frequency (HF) radio. In our setup, we assume to have telephone recordings of speakers for training, but recordings of different channels for testing with varying (lower) signal quality. Starting from a Gaussian mixture / support vector machine (GMM/SVM) baseline, we evaluate multi-condition training (MCT), an ideal channel classification approach (ICC), and nuisance attribute projection (NAP) to compensate for the loss of information due to the transmission. In an evaluation on Switchboard-2 data using Skype and HF channel simulators, we show that, for good signal quality, NAP improves the baseline system performance from 5% EER to 3.33% EER (for both Skype and HF). For strongly distorted data, MCT or, if adequate, ICC turn out to be the method of choice.