The success of deep learning in recent years has arguably been driven by the availability of large datasets for training powerful predictive algorithms. In medical applications however, the sensitive nature of the data limits the collection and exchange of large-scale datasets. Privacy-preserving and collaborative learning systems can enable the successful application of machine learning in medicine. However, collaborative protocols such as federated learning require the frequent transfer of parameter updates over a network. To enable the deployment of such protocols to a wide range of systems with varying computational performance, efficient deep learning architectures for resource-constrained environments are required. Here we present MoNet, a small, highly optimized neural-network-based segmentation algorithm leveraging efficient multi-scale image features. MoNet is a shallow, U-Net-like architecture based on repeated, dilated convolutions with decreasing dilation rates. We apply and test our architecture on the challenging clinical tasks of pancreatic segmentation in computed tomography (CT) images as well as brain tumor segmentation in magnetic resonance imaging (MRI) data. We assess our model's segmentation performance and demonstrate that it provides performance on par with compared architectures while providing superior out-of-sample generalization performance, outperforming larger architectures on an independent validation set, while utilizing significantly fewer parameters. We furthermore confirm the suitability of our architecture for federated learning applications by demonstrating a substantial reduction in serialized model storage requirement as a surrogate for network data transfer. Finally, we evaluate MoNet's inference latency on the central processing unit (CPU) to determine its utility in environments without access to graphics processing units. Our implementation is publicly available as free and open-source software.