S U M M A R YGlobal earthquake locations are often associated with very large systematic travel-time residuals even for clear arrivals, especially for regional and near-regional stations in subduction zones because of their strongly heterogeneous velocity structure. Travel-time corrections can drastically reduce travel-time residuals at regional stations and, in consequence, improve the relative location accuracy. We have extended the shrinking-box source-specific station terms technique to regional and teleseismic distances and adopted the algorithm for probabilistic, nonlinear, global-search location. We evaluated the potential of the method to compute precise relative hypocentre locations on a global scale. The method has been applied to two specific test regions using existing P-and pP-phase picks. The first data set consists of 3103 events along the Chilean margin and the second one comprises 1680 earthquakes in the Tonga-Fiji subduction zone. Pick data were obtained from the GEOFON earthquake bulletin, produced using data from all available, global station networks. A set of timing corrections varying as a function of source position was calculated for each seismic station. In this way, we could correct the systematic errors introduced into the locations by the inaccuracies in the assumed velocity structure without explicitly solving for a velocity model. Residual statistics show that the median absolute deviation of the travel-time residuals is reduced by 40-60 per cent at regional distances, where the velocity anomalies are strong. Moreover, the spread of the travel-time residuals decreased by âŒ20 per cent at teleseismic distances (>28 âą ). Furthermore, strong variations in initial residuals as a function of recording distance are smoothed out in the final residuals. The relocated catalogues exhibit less scattered locations in depth and sharper images of the seismicity associated with the subducting slabs. Comparison with a high-resolution local catalogue reveals that our relocation process significantly improves the hypocentre locations compared to standard locations.