Air extracted from polar ice allows reconstruction of atmospheric levels of CO2 prior to direct atmospheric measurements. These ice core records are commonly used to infer information about past variability of CO2 fluxes. Due to processes involved in storing 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 some time scales. With a numerical model of the firn processes we quantify this smoothing, and discuss implications for inferring CO2 flux variability from the high time resolution Law Dome ice core record. In particular we look at results from the CCMLP model intercomparison of terrestrial models over the 20th century. The firn model smoothes concentrations more than a 10-year running mean does, so conclusions about how well the results match the ice core record require careful consideration of the smoothing.