Global average estimates of the group velocity and attenuation of long-period (120--300 s) Rayleigh waves were made using seismograms from the epicenter's antipode (Δ~180¿). Focusing at the antipode produced amplified arrivals with favorable signal-to-noise ratios. The high-quality data yielded very stable attenuation values, with excellent agreement between the results from successive Rayleigh arrivals for a single event and between the results for two different events. Lateral heterogeneities in earth structure can cause systematic biasing of attenuation measurements based on antipodal records. The initial, uncorrected results therefore provide a lower bound estimate of global Q. An ellipsoidal perturbation in shape was used to simulate the effects of lateral velocity heterogeneities on Rayleigh wave propagation. Using the agreement of repeated attenuation measurements as a constraint, we estimated both the bias in those measurements and the splitting widths of the Rayleigh modes. At a period of 200 s, the estimated splitting width is 0.30%; this agrees closely with calculations by Luh (1974) for an earth model with different continental and oceanic velocity profiles. The estimated bias varied from 30% to zero over the 120- to 260-s band. After correcting for bias, the antipodal Q values range from 108 at 120 s to 188 at 260 s. These Q are within the range of previous measurements but are lower than the mean values from typical great circle studies, implying that the globally averaged upper mantle is slightly more attenuative than has been generally recognized.