We present a novel depth from focus technique. Following prior work, our pipeline starts with a focal stack and an estimation of the amount of defocus as given by, for instance, the Ring Difference Filter. To improve robustness to outliers while avoiding to rely on costly non-linear optimizations, we propose an original scheme that linearly scans the profile over a fixed size window, searching for the best peak within each window using a linearized least-squares Laplace regression. As a post-process, depth estimates with low confidence are reconstructed though an adaptive Moving Least Squares filter. We show how to objectively evaluate the performance of our approach by generating synthetic focal stacks from which the reconstructed depth maps can be compared to ground truth. Our results show that our method achieves higher accuracy than previous non-linear Laplace regression technique, while being orders of magnitude faster.