Neurons respond to sensory stimuli by altering the rate and temporal pattern of action potentials. These spike trains both encode and propagate information that guides behavior. Local inhibitory networks can affect the information encoded and propagated by neurons by altering correlations between different spike trains. Correlations introduce redundancy that can reduce encoding but also facilitate propagation of activity to downstream targets. Given this trade-off, how can networks maximize both encoding and propagation efficacy? Here, we examine this problem by measuring the effects of olfactory bulb inhibition on the pairwise statistics of mitral cell spiking. We evoked spiking activity in the olfactory bulb in vitro and measured how lateral inhibition shapes correlations across timescales. We show that inhibitory circuits simultaneously increase fast correlation (i.e., synchrony increases) and decrease slow correlation (i.e., firing rates become less similar). Further, we use computational models to show the benefits of fast correlation/slow decorrelation in the context of odor coding. Olfactory bulb inhibition enhances population-level discrimination of similar inputs, while improving propagation of mitral cell activity to cortex. Our findings represent a targeted strategy by which a network can optimize the correlation structure of its output in a dynamic, activity-dependent manner. This trade-off is not specific to the olfactory system, but rather our work highlights mechanisms by which neurons can simultaneously accomplish multiple, and sometimes competing, aspects of sensory processing.