We exploit archived salinity data, averaged by month for the years 1995--2001, to evaluate exchange of salt between Long Island Sound and shelf waters, and treat Long Island Sound as a control volume with eastern and western boundaries at The Race and the East River, respectively. The use of inverse methods to solve a system of equations expressing conservation of salt and water provides estimates of model parameters together with uncertainty estimates and measures of model performance. We explore the use of a single exchange coefficient acting on an axial salinity gradient to represent exchange at The Race and find that it is necessary to allow the coefficient to depend weakly on variability of freshwater discharge, R, into the sound, i.e., KxRace = ($frac{{rm R}}{leftlangle {rm R} rightrangle}$)0.2(1,600 ¿ 200) m2/s. Using established estimates of the mean circulation at the western boundary of the sound, we determine a dispersion coefficient in the Upper East River of 300 ¿ 200 m2/s. Explicitly modeling the advective exchange flow (gravitational circulation) at The Race using a coefficient that varies as the one-third power of the normalized discharge indicates that gravitational circulation accounts for less than 10% of the up-estuary salt flux in eastern Long Island Sound.