Abstract-In this paper we propose a novel approach to implement multiplierless unity-gain SDF FFTs. Previous methods achieve unity-gain FFTs by using either complex multipliers or non-unity-gain rotators with additional scaling compensation. Conversely, this paper proposes unity-gain FFTs without compensation circuits, even when using non-unity-gain rotators. This is achieved by a joint design of rotators so that the entire FFT is scaled by a power of two, which is then shifted to unity. This reduces the amount of hardware resources of the FFT architecture, while having high accuracy in the calculations. The proposed approach can be applied to any FFT size and various designs for different FFT sizes are presented.