Ice core records are commonly used to infer information about past variability of CO₂ fluxes. Because of processes involved in enclosing this air in ice, ice core records are a smoothed representation of the actual past atmospheric variations. As such, there is a limit to how much information ice core measurements can contain about flux variability on short timescales. With a numerical model of the firn processes we quantify this smoothing and describe how it can be reproduced with pulse response functions. We generate and make available pulse response functions for CO₂ at the DE08 site on Law Dome, Antarctica. We discuss implications of the smoothing for inferring CO₂ flux variability from the Law Dome ice core record. In particular we look at results from an intercomparison of terrestrial biosphere models over the twentieth century and show how much of the CO₂ variability would be reflected in the Law Dome ice core record. We also smooth atmospheric δ¹³CO₂ from a study that compared fixed and varying isotopic discrimination. We find that the impact of changing discrimination, shown previously to be large on interannual timescales, is small on the decadal scales accessible from ice core records.