This work shows the effect of the use of moderating layers on the sodium void effect in sodium-cooled, mixed oxide-fueled fast breeder reactors. The moderating layers consist of either zirconium boride ZrB2 or zirconium hydride ZrH2. The two investigated ZrH2 layers (0.1 and 0.2 mm thick) cause a strong reduction of the sodium void effect. Additionally, these layers significantly improve the fuel temperature effect and the coolant effect of the system. All changes caused by the insertion of the ZrH2 layers result in a significantly increased stability of the fast reactor system against transients. The moderating layers have only a small influence on the breeding effect and on the production of minor actinides. The effect in the infinite system can be fully combined with the traditional methods of increasing the neutron leakage.