The Caribbean Sea is selected as a region where the large-scale circulation is well determined by historical hydrographic measurements through application of the inverse method. A simple example is used to illustrate the technique and to demonstrate how some physically relevant quantities may be well determined in the formally underdetermined inverse problem. The geostrophic flow field in the Caribbean is found by imposing mass and salt conservation constraints in seven layers separated by surfaces of constant potential density. An unsmoothed solution is displayed that has weak dependence on an initial choice of reference level. In addition, a unique smoothed solution is shown. Above &sgr;ϑ = 27.4, the total flow leaving the western Caribbean is estimated to be 29¿106 m3 s-1, in agreement with direct measurements. This flow is made up of 22¿106 m3s -1 entering the Caribbean from the east and flowing across the southern half of the basin as the Caribbean Current, and 7¿106 m3 s-1, in agreement with direct measurements. This flow is made up of 22¿106 m3 s-1 entering the Caribbean from the east and flowing across the southern half of the basin as the Caribbean Current, and 7¿107 m3 s-1 entering from the north through Windward Passage. Both of these currents show small-scale variability that diminishes with distance from the respective passages. The deep flow has no net transport, as required by the shallow exit, but a well organized clockwise recirculation is found in the deep eastern Caribbean.