Image watermarking has been the topic of much research and it is now widely accepted that the watermark should be placed in perceptually significant components of an image, in order to be robust against common signal distortions and malicious attacks. This choice makes the watermark potentially visible, therefore only slight modifications to the original image are allowed with a low loss of quality. In this work we propose a scheme where the energy of the watermark embedded depends on the image to be marked, thus fitting image capacity. The three fundamental stages of our scheme are: a watermark sequence generation as zero-mean, unit-variance Gaussian noise, an embedding procedure working in the DWT domain, and watermark detection performed by correlation and not requiring the original image. The experimental results prove that the method is resistant to JPEG compression up to a quality factor of 10%, to blurring and median filtering, to cropping and stretching; moreover the watermark is not perceivable for many different kinds of images, including cartoons.