We use an inverse method to compute the deep circulation in the eastern South Pacific Ocean, on isopycnal layers within the depth range of 1,000–3,000 m. The method gives probability density functions of the isopycnal and diapycnal velocities and diffusivities on a grid with a realistic eastern boundary, based on tracer fields. An oxygen consumption rate, assumed spatially constant, controls the solution effectiveness (minimum value of the model cost function) and the magnitude of the diffusivities. The isopycnal circulation is, by contrast, less dependent on the consumption rate. Direct deep float displacement data is used as a check on our solutions rather than a constraint. The model circulation agrees broadly with this independent data. Where the computed circulation does not agree, we argue that it is mainly because of different sampling, model resolution and model assumptions. The isopycnal circulation below 1,000 dbar is dominated by zonal flows and topographically controlled structures. A westward helium plume at 15°S seen on δ3He maps is reproduced by the model but is less intense than expected by the β-plume theory. The model did not find correlations between the diapycnal forcing and the known volcanically active part of the EPR, suggesting that the net large-scale effect of heating along the ridge on the circulation is small over the basin as a whole. Eastern boundary flow along the coast of South America appears as a main exit route for deep water, but the flow shows broader scales than suggested in previous studies, possibly due to the resolution of the model. The deep outflow of the southeastern Pacific is associated in the model with isopycnal PV stretching, rather than a Stommel-Arons (diapycnal) balance.