Data from a hydrographic survey of the Tunisia-Sardinia-Sicily region are assimilated into a primitive equations ocean model. The model simulation is then averaged in time over the short duration of the data survey. The corresponding results, consistent with data and dynamics, are providing new insight into the circulation of Modified Atlantic Water (MAW) and Levantine Intermediate Water (LIW) in this region of the western Mediterranean. For MAW these insights include a southward jet off the east coast of Sardinia, anticyclonic recirculation cells on the Algerian and Tunisian shelves, and a secondary flow splitting in the Strait of Sicily. For the LIW regime a detailed view of the circulation in the Strait of Sicily is given, indicating that LIW proceeds from the strait to the Tyrrhenian Sea. No evidence is found for a direct current path to the Sardinia Channel. Complex circulation patterns are validated by two-way nesting of critical regions. Volume transports are computed for the Strait of Sicily, the Sardinia Channel, and the passage between Sardinia and Sicily.