Center-surround receptive fields are a fundamental unit of brain organization. It has been proposed that olfactory bulb mitral cells exhibit this functional circuitry, with excitation from one glomerulus and inhibition from a broad field of glomeruli within reach of the lateral dendrites. We investigated this hypothesis using a combination of in vivo intrinsic imaging, single-unit recording, and a large panel of odors. Assuming a broad inhibitory field, a mitral cell would be influenced by >100 contiguous glomeruli and should respond to many odors. Instead, the observed response rate was an order of magnitude lower. A quantitative model indicates that mitral cell responses can be explained by just a handful of glomeruli. These glomeruli are spatially dispersed on the bulb and represent a broad range of odor sensitivities. We conclude that mitral cells do not have center-surround receptive fields. Instead, each mitral cell performs a specific computation combining a small and diverse set of glomerular inputs.