The distributions of temperature, oxygen and potential vorticity on two isopycnals and the geostrophic shear between them are used to obtain the flow fields and diffusivities through a least-squares inversion of the steady state, advective-diffusive equations. The source of the data is the Levitus Atlas, and the two isopycnals are located in a 24° square centered on the Mediterranean Water tongue in the eastern North Atlantic. One isopycnal is in the thermocline and the other beneath so chosen to be near the level of maximum salinity and temperature anomaly.Although tracer distributions on the two levels are similar, the inversion suggests that they result from quite different processes. In the thermocline a warm, salty tongue protrudes into the subtropical gyre and results from downward diffusion of heat and salt in the north and lateral exchange with Antarctic Intermediate Water in the south. At the true Mediterranean Water level the flow is down the direction of the tongue and the advective flux is balanced by a lateral diffusive flux.The least-squares technique gives estimates for the streamfunction which are quite insensitive to some of the subjective choices that must be made while the diffusion coefficients are relatively more sensitive. In particular, in order to overdetermine the problem the cross-isopycnal variation of the cross-isopycnal diffusivity must be constrained. A method based on the difference in values between the two levels reduces the residual variance substantially more than one based on Gargett's (1984) Brunt-Väisälä frequency dependence.