Many subsurface passages connecting the deep parts of the oceans have a topography such that the location of the most pronounced horizontal constriction does not coincide with that of the sill. When applying rotating hydraulic theory to describe the deep water flow through channels of this type, a problematic situation emerges since the standard analysis assumes a well-defined controlling section. The present study demonstrates how the associated critical flow problem arising from the hydraulic model may be resolved on the basis of functional-theoretical analysis. The methodology is applied to the deep water flow into the Baltic proper through the Bornholm Channel, where multiple critical cross sections were found. These, as well as the associated critical transport predictions, are discussed, and it is found that only one of them serves de facto as a control with unidirectional flow. ¿ 2000 American Geophysical Union