In this study we use the consistency conditions of the Radon transform to aid attenuation correction in PET. The conditions are used both for estimating the parameters of a uniform elliptical attenuation distribution (without any transmission measurements) and for correcting for patient motion between the transmission and emission acquisitions. The results show that, for a uniform elliptical attenuation distribution, the reconstructed count densities obtained using attenuation correction based on the consistency conditions are within 1% of the true values. The method is shown to be fairly tolerant to the effects of photon counting statistics and to small non-uniformities in the attenuation distribution (such as skull attenuation). The results also show that the consistency conditions may be useful in correcting for patient motion. The method is shown to effectively compensate for shifts in two dimensions using both simulated and experimental data.