Since most tomographic problems deal with imperfect data coverage and noisy data, an estimate of the seismic velocity in the Earth can only be a local average of the ‘true’ velocity with some attached uncertainty. We use the SOLA (subtractive optimally localized averages) method, a Backus–Gilbert-type method based on the resolution–uncertainty trade-off, to build a range of models of Rayleigh-wave velocities in the Pacific upper mantle. We choose one solution and show how to analyse the model using its resolution and uncertainties. We exploit the model statistics to evaluate the significance of deviations from a theoretical prediction: a half-space cooling model of the Pacific lithosphere. We investigate a slow-velocity anomaly located northeast of Hawaii, at about 200 km depth, and a pattern of alternatively slow- and fast-velocity bands, aligned approximately northwest to southeast, between 200 and 300 km depth. According to our resolution and uncertainty analyses, both features seem to be resolved.