Fixed-quality image compression is a coding paradigm where the tolerated introduced distortion is set by the user. This article proposes a novel fixed-quality compression method for remote sensing images. It is based on a neural architecture we have recently proposed for multirate satellite image compression. In this article, we show how to efficiently estimate the reconstruction quality using an appropriate statistical model. The performance of our approach is assessed and compared against recent fixed-quality coding techniques and standards in terms of accuracy and rate-distortion, as well as with recent machine learning compression methods in rate-distortion, showing competitive results. In particular, the proposed method does not introduce artifacts even when coding neighboring areas at different qualities