The olfactory system is capable of detecting odorants at very low concentrations. Physiological experiments have demonstrated odorant sensitivities down to the picomolar range in preparations from the sensory epithelium. However, the contemporary model for olfactory signal transduction provides that odorants bind to olfactory receptors with relatively low specificity and consequently low affinity, making this detection of low-concentration odorants theoretically difficult to understand. We employ a computational model to demonstrate how olfactory sensory neuron (OSN) sensitivity can be tuned by modulation of receptor-effector coupling and/or by other mechanisms regulating spare receptor capacity, thus resolving this conundrum. The EC10-90 intensity tuning ranges (ITRs) of whole olfactory glomeruli and postsynaptic mitral cells are considerably broader than the commensurate ITRs of individual OSNs. These data are difficult to reconcile with certain contemporary hypotheses that convergent OSNs in mammals exhibit a homogeneous population of olfactory receptors and identical tuning for odor stimuli. We show that heterogeneity in spare receptor capacities within a convergent OSN population can increase the ITR (EC10-90) of a convergent population of OSNs regardless of the presence or absence of a diversity of receptor expression within the population. The modulation of receptor-effector coupling has been observed in OSNs; other mechanisms for cellular regulation of spare receptor capacity are also highly plausible (e.g., quantitative regulation of the relative expression levels of receptor and effector proteins). We present a model illustrating that these processes can underlie both how OSNs come to exhibit high sensitivity to odorant stimuli without necessitating increased ligand-receptor binding affinities or specificities and how a population of convergent OSNs could exhibit a broader concentration sensitivity than its individual constituent neurons, even given a population expressing identical odorant receptors. The regulation of spare receptor capacity may play an important role in the olfactory system's ability to reliably detect low odor concentrations, discriminate odor intensities, and segregate this intensity information from representations of odor quality.