This theoretical paper shows how the average mass-transfer coefficient in a hollow-fiber module can be estimated from the average properties of the hollow fibers. The analysis assumes that each solute diffuses independently, and that solute transport is unaffected by mass-transfer resistances on the permeate side of the membrane. For polydisperse fiber diameters, the average coefficient is reduced by the polydispersity; for polydisperse fiber-wall thicknesses, the average coefficient can be increased or decreased. The change in this average coefficient depends on the fraction of solute transferred, i.e. on the ’clearance’. It will have different values for different solutes. The results have bearing on the design of artificial kidneys.