Abstract: Shadow aliasing due to limited storage precision has been plaguing discrete shadowing algorithms for decades. We present a simple method to eliminate false self-shadowing through adaptive depth bias. Unlike existing methods which simply set the weight of the bias based on surface slope or utilize the second nearest surface, we evaluate the bound of bias for each fragment and compute the optimal bias within the bound. Our method introduces small overhead, preserves more shadow details than widely used constant bias and slope scale bias and works for common 2D shadow maps as well as 3D binary shadow volumes.