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An important constraint on mechanisms of past carbon cycle variability is provided by the stable isotopic composition of carbon in atmospheric carbon dioxide (δ¹³C-CO₂) trapped in polar ice cores, but obtaining very precise measurements has proven to be a significant analytical challenge. Here we describe a new technique to determine the δ¹³C of CO₂ at very high precision, as well as measuring the CO₂ and N₂O mixing ratios. In this method, ancient air is extracted from relatively large ice samples (~400 g) with a dry-extraction "ice grater" device. The liberated air is cryogenically purified to a CO₂ and N₂O mixture and analyzed with a microvolume-equipped dual-inlet IRMS (Thermo MAT 253). The reproducibility of the method, based on replicate analysis of ice core samples, is 0.02‰ for δ¹³C-CO₂ and 2 ppm and 4 ppb for the CO₂ and N₂O mixing ratios, respectively (1σ pooled standard deviation). Our experiments show that minimizing water vapor pressure in the extraction vessel by housing the grating apparatus in a ultralow-temperature freezer (−60 °C) improves the precision and decreases the experimental blank of the method to −0.07 ± 0.04‰. We describe techniques for accurate calibration of small samples and the application of a mass-spectrometric method based on source fragmentation for reconstructing the N₂O history of the atmosphere. The oxygen isotopic composition of CO₂ is also investigated, confirming previous observations of oxygen exchange between gaseous CO₂ and solid H₂O within the ice archive. These data offer a possible constraint on oxygen isotopic fractionation during H₂O and CO₂ exchange below the H₂O bulk melting temperature.