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Interference is a central feature of the wireless channel. However, in many cases, the interferer's activity can be bursty and it is overly pessimistic to assume that interference is always present. In this paper, we use a degraded message set formulation of the two-user interference channel to study the statistical gains that can be harnessed from bursty interference. We consider a linear deterministic model of the Gaussian interference channel and characterize the degraded message set capacity region.