We compared the concentration dependence of the ability of rats to identify odorants with the calcium signals in the nerve terminals of the olfactory receptor neurons. Although identification performance decreased with concentrations both above and below the training stimuli it remained well above random at all concentrations tested (between 0.0006% and 35% of saturated vapor). In contrast, the calcium signals in the same awake animals were much smaller than their maximum values at odorant concentrations <1% of saturated vapor. In addition, maps of activated glomeruli changed dramatically as odorant concentration was reduced. Thus perceptual stability exists in the face of dramatic changes in both the amplitude and the maps of the input to the olfactory bulb. The data for the concentration dependence of the response of the most sensitive glomeruli for each of five odorants was fitted with a Michaelis–Menten (Hill) equation. The fitted curves were extrapolated to odorant concentrations several orders of magnitude lower the smallest observed signals and suggest that the calcium response at low odorant concentrations is > 1000 times smaller than the response at saturating odorant concentrations. We speculate that only a few spikes in olfactory sensory neurons may be sufficient for correct odorant identification.