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The gills of most teleost fishes are covered by plate-like structures, the secondary lamellae, that provide the bulk of the respiratory surface area. Water passing over the secondary lamellae exchanges gases with blood passing through the secondary lamellae, forming a system that has served as a classic model of counter-current exchange. In this study, a computational model of flow around the secondary lamellae is used to examine the hydrodynamic consequences of changes to the lamellar morphology. Consistent with previous studies, the interlamellar distance is found to strongly affect the hydrodynamic resistance of the gills. However, the presence of a small gap between the tips of the secondary lamellae is found to have a similarly strong effect on the hydrodynamic resistance and flow patterns within the gills. The results from this model have been generally formulated, allowing the calculation of the hydrodynamic resistance for measured morphometric parameters. These results provide a new basis for comparing theoretical predictions of the gill resistance with measured values, and provide a general model for examining the diversity gill morphologies observed in teleost fishes.