Lattice diffusion coefficients have been determined for 19 elements (Li, Be, Na, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Y, Zr, Eu, Gd, Lu and Hf) in a single crystal of San Carlos olivine as a function of crystallographic orientation, at 1,300°C, 1 bar and fO2 = 10-8.3 bars, by equilibration with a synthetic silicate melt. Results for Li, Na, V, Cr, Fe and Zn are from diffusion of these elements out of the olivine, starting from their indigenous concentrations; those for all other elements are from diffusion into the olivine, from the silicate melt reservoir. Our 25-day experiment produced diffusion profiles 50 to > 700 µm length, which are sufficiently long that precise analyses could be achieved by scanning laser ablation inductively coupled plasma mass spectrometry, even at concentration levels well below 1 µg g-1. For the divalent cations Ca, Mn, Fe and Ni, profiles were also obtained by electron microprobe analysis. The results of the two methods agree well with each other, and are consistent with divalent cation diffusion coefficients previously determined using different experimental methodologies. Olivine/melt partition coefficients retrieved from the data are also consistent with other published partitioning data, indicating that element incorporation and transport in olivine in our experiment occurred via mechanisms appropriate to natural conditions. Most of the examined trace elements diffuse through olivine at similar rates to the major octahedral cations Fe and Mg, showing that cation charge and radius have little direct influence on diffusion rates. Aluminium and P remain low and constant in the olivine, implying negligible transport at our analytical scale, hence Al and P diffusion rates that are at least two orders of magnitude slower than the other cations studied here. All determined element diffusivities are anisotropic, with diffusion fastest along the  axis, except Y and the REEs, which diffuse isotropically. The results suggest that element diffusivity in olivine is largely controlled by cation site preference, charge balance mechanisms and point-defect concentrations. Elements that are present on multiple cation sites in olivine (e.g. Be and Ti) and trivalent elements that are charge-balanced by octahedral site vacancies tend to diffuse at relatively fast rates.