In this work we propose a discussion and detailed implementation of a very simple gradient domain method that tries to eliminate the effect of nonuniform illumination and at the same time preserves the images details. This model, which to the best of our knowledge has not been explored in spite of its simplicity, acts as a high pass filter. We show that with a single contrast parameter (which keeps the same value in most experiments), the model delivers state of the art results. They compare favorably to results obtained with more complex algorithms. Our algorithm is designed for all kinds of images, but with the special specification of making minimal image detail alteration thanks to a first order fidelity term, instead of the usual zero order term. Experiments on non-uniform medical images and on hazy images illustrate significant perception gain.