In odorant-rich environments, animals must be able to detect specific odorants of interest against variable backgrounds. However, studies have found that both humans and rodents are poor at analyzing the components of odorant mixtures, suggesting that olfaction is a synthetic sense in which mixtures are perceived holistically. We found that mice could be easily trained to detect target odorants embedded in unpredictable and variable mixtures. To relate the behavioral performance to neural representation, we imaged the responses of olfactory bulb glomeruli to individual odors in mice expressing the Ca(2+) indicator GCaMP3 in olfactory receptor neurons. The difficulty of segregating the target from the background depended strongly on the extent of overlap between the glomerular responses to target and background odors. Our study indicates that the olfactory system has powerful analytic abilities that are constrained by the limits of combinatorial neural representation of odorants at the level of the olfactory receptors.