Rotating two-layer exchange flow over a sill in a strait separating two relatively deep and wide basins is analyzed. Upstream of the sill in the deep upstream basin, the infinitely deep dense lower layer is assumed to be inactive, while the relatively thin upper layer flowing away from the sill forms a detached boundary current in the upstream basin. This analysis emphasizes the importance of this upstream boundary current, incorporating its width as a key parameter in a formalism for deducing the volume exchange rate and discriminating between maximal and submaximal states. Hence, even for narrow straits in which rotation does not dominate the dynamics within the strait, the importance of rotation in the wide upstream basin can be exploited. It is shown that the maximal allowable exchange transport through straits wider than 1½ Rossby deformation radii increases as rotation increases, unlike for smaller rotations, where the exchange decreases as rotation increases. The theory is applied to the exchange flow through the Strait of Gibraltar. This application illustrates how images of the oceans taken from space showing the width of the upstream flow, in this case a space shuttle photograph, might be used to determine the exchange transport through a strait. Maximal exchange conditions in the Strait of Gibraltar are predicted to apply at the time the space shuttle photograph was taken.