Sensory systems adapt their neural code to changes in the sensory environment, often on multiple time scales. Here, we report a new form of adaptation in a first-order auditory interneuron (AN2) of crickets. We characterize the response of the AN2 neuron to amplitude-modulated sound stimuli and find that adaptation shifts the stimulus-response curves toward higher stimulus intensities, with a time constant of 1.5 s for adaptation and recovery. The spike responses were thus reduced for low-intensity sounds. We then address the question whether adaptation leads to an improvement of the signals representation and compare the experimental results with the predictions of two competing hypotheses: infomax, which predicts that information conveyed about the entire signal range should be maximized, and selective coding, which predicts that foreground signals should be enhanced while background signals should be selectively suppressed. We test how adaptation changes the input-response curve when presenting signals with two or three peaks in their amplitude distributions, for which selective coding and infomax predict conflicting changes. By means of Bayesian data analysis, we quantify the shifts of the measured response curves and also find a slight reduction of their slopes. These decreases in slopes are smaller, and the absolute response thresholds are higher than those predicted by infomax. Most remarkably, and in contrast to the infomax principle, adaptation actually reduces the amount of encoded information when considering the whole range of input signals. The response curve changes are also not consistent with the selective coding hypothesis, because the amount of information conveyed about the loudest part of the signal does not increase as predicted but remains nearly constant. Less information is transmitted about signals with lower intensity.