Recently, Bijwaard et al. (JGR, 1998) constructed a high-resolution global tomography model, mapping upper mantle structure with detail (60-100 km) directly comparable with that obtained in regional studies. This was achieved through the exploitation of an accurate global data set of 7.6 million P and pP phases and the implementation of a model parameterization with cell sizes adapted to the amount of ray sampling. However, the in principle nonlinear tomography problem was up to now linearized about the ray paths in the 1-D reference Earth model used. The bending of rays due to lateral heterogeneity has therefore been ignored, although this may be very important when imaging small-scale structure. Here, we shall present results obtained from a nonlinear approach. For this purpose the entire global data set of P and pP phases was raytraced through the (3-D) model obtained by linearized tomography and new travel-time residuals were calculated and subsequently inverted. The nonlinear results indicate that the improvement of the linear results is small, but significant in regions with high-amplitude heterogeneity. We observe enhanced focussing and higher amplitudes which may be promising for further nonlinear iterations.