14CO2 produced in the atmosphere by nuclear weapons testing in the 1960's is now incorporated in the air bubbles of Antarctic ice. The high atmospheric radiocarbon growth rates through the period of tests and subsequent decline provide a unique and independent test for the smoothing of atmospheric CO2 signals due to firn diffusion and bubble close off. The level of smoothing quantifies the time resolution with which atmospheric trace gas histories can be reconstructed from ice cores. In this paper, the methodologies for the preparation and AMS measurements of ice core and firn 14CO2 from high accumulation sites at Law Dome are detailed. The results are compared with predictions of a numerical model incorporating firn air diffusion and bubble close-off. The sample sizes, precision of measurements and sources of contamination are discussed for both firn and ice samples.