The three-dimensional shear attenuation, or Q¿, structure of the upper mantle is still poorly understood despite the increasing accuracy and sophistication of velocity models of the same part of the Earth. Here we present a set of three-dimensional Q¿ models of the upper mantle based on amplitude measurement of minor and major arc Rayleigh waves in the period range 70--170 s. The models show that areas of low attenuation underlie continents to a depth of around 300 km and areas of high attenuation are associated with oceans and plate boundaries, particularly in the top 200 km. Below ~350 km, the sensitivity of the data to attenuation structure decreases rapidly. It is well known that the amplitudes of surface waves can be strongly influenced by factors other than attenuation, in particular, focusing due to elastic structure and errors in source mechanisms. We consider the effects of focusing by discussing the implications of the results of Selby and Woodhouse <2000>. Comparisons with focusing predictions using phase velocity maps allow us to identify features due to focusing in maps of attenuation distribution. The influence of the source on the observed attenuation distribution is investigated by including a source term in the model inversion. We find that successfully combining the data at each frequency into one three-dimensional model requires that this source term must vary with frequency, suggesting that a simple correction to the scalar moment of each event cannot explain the observations. Although the effects of focusing and the source can be significant, we find that the observed attenuation pattern is robust up to degree 8; however, shorter-wavelength structure can be strongly influenced by other controls. Finally, we use one of the models to predict the degree 2 attenuation pattern for 250-s Rayleigh waves. The observed pattern suggests that existing normal mode observations may be explainable in terms of structure above 350 km depth.