The study of information transmission by neural spike trains is a hard problem, but one that can be made easier by examining only the low-order statistical structure of the spike trains. We have previously found an expression relating the mutual information to up to pairwise correlations among spikes, and have recently extended this approach to arbitrary order, thus incorporating n-wise correlations. An application in which this is of particular interest is thalamocortical information transmission, in which relay cells switch between a structured, "bursting" mode of spike firing, and a relatively unstructured or "tonic" firing mode. Making use of an "Integrate-and-Fire-or-Burst" model (Smith, Cox, Sherman & Rinzel 2000), we use our approach to ask what the effect of bursting is on information transmission, and how it decomposes into firing rate and correlational contributions.