When approaching a novel visual recognition problem in a specialized image domain, a common strategy is to start with a pre-trained deep neural network and fine-tune it to the specialized domain. If the target domain covers a smaller visual space than the source domain used for pre-training (e.g. ImageNet), the fine-tuned network is likely to be over-parameterized. However, applying network pruning as a post-processing step to reduce the memory requirements has drawbacks: fine-tuning and pruning are performed independently; pruning parameters are set once and cannot adapt over time; and the highly parameterized nature of state-of-the-art pruning methods make it prohibitive to manually search the pruning parameter space for deep networks, leading to coarse approximations. We propose a principled method for jointly fine-tuning and compressing a pre-trained convolutional network that overcomes these limitations. Experiments on two specialized image domains (remote sensing images and describable textures) demonstrate the validity of the proposed approach.