One of the main limitations to the adoption of deep learning for image compression is the need to train multiple models to compress at multiple rates. In the case of onboard remote sensing data compression, another limitation is the computational cost of the neural networks. Addressing both limitations, this letter presents a new reduced-complexity architecture for multirate compression of remote sensing images. The proposed architecture enables compressing at a precise user-selected rate while keeping a competitive performance in lossy compression on different sets of remote sensing data. The proposed approach is amenable for onboard deployment.