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Nanocrystalline soft magnetic materials have been developed possessing a wide variety of compositions designed to reduce losses and a high saturation induction. Nanocrystalline soft magnetic alloys with compositions (Fe1-x-yCoxNiy)89-zZr7B4Cuz were prepared by the isothermal annealing of melt-spun ribbons. The ribbon samples were characterized by the following techniques: differential thermal analysis, X-ray diffraction, transmission electron microscopy, and vibrating sample magnetometry. Several alloys have been shown to have near-zero magnetostriction. Alloy design, synthesis, and properties of these alloys will be discussed.