In this paper we address the memory demands that come with the processing of 3-dimensional, high-resolution, multi-channeled medical images in deep learning. We exploit memory-efficient backpropagation techniques, to reduce the memory complexity of network training from being linear in the network’s depth, to being roughly constant – permitting us to elongate deep architectures with negligible memory increase. We evaluate our methodology in the paradigm of Image Quality Transfer, whilst noting its potential application to various tasks that use deep learning. We study the impact of depth on accuracy and show that deeper models have more predictive power, which may exploit larger training sets. We obtain substantially better results than the previous state-of-the-art model with a slight memory increase, reducing the root-mean-squared-error by 13%. Our code is publicly available.