Adaptation of the spike-frequency response to constant stimulation, as observed on various timescales in many neurons, reflects high-pass filter properties of a neuron's transfer function. Adaptation in general, however, is not sufficient to make a neuron's response independent of the mean intensity of a sensory stimulus, since low frequency components of the stimulus are still transmitted, although with reduced gain. We here show, based on an analytically tractable model, that the response of a neuron is intensity invariant, if the fully adapted steady-state spike-frequency response to constant stimuli is independent of stimulus intensity. Electrophysiological recordings from the AN1, a primary auditory interneuron of crickets, show that for intensities above 60 dB SPL (sound pressure level) the AN1 adapted with a time-constant of approximately 40 ms to a steady-state firing rate of approximately 100 Hz. Using identical random amplitude-modulation stimuli we verified that the AN1's spike-frequency response is indeed invariant to the stimulus' mean intensity above 60 dB SPL. The transfer function of the AN1 is a band pass, resulting from a high-pass filter (cutoff frequency at 4 Hz) due to adaptation and a low-pass filter (100 Hz) determined by the steady-state spike frequency. Thus, fast spike-frequency adaptation can generate intensity invariance already at the first level of neural processing.