The magnetic and structural properties of ion beam sputtered Fe/CoNbZr multilayers were studied as a function of the CoNbZr and Fe layer thickness. Good soft-magnetic properties (coercivity <40 A/m and permeability >1000) are obtained only when the Fe grains are small, which is the case for multilayers with Fe layer thicknesses below 10 nm and CoNbZr layer thicknesses above 4 nm. Thick CoNbZr layers (>4 nm) are amorphous and repeated nucleation of Fe grains is observed. When the CoNbZr layers are too thin (<3 nm) they are crystalline and do not interrupt the Fe grain growth. The resulting columnar growth of Fe throughout the total film thickness leads then to a drastic decrease of permeability and increase of coercivity.