Semantic segmentation by convolutional neural networks (CNN) has advanced the state of the art in pixel-level classification of remote sensing images. However, processing large images typically requires analyzing the image in small patches, and hence features that have large spatial extent still cause challenges in tasks such as cloud masking. To support a wider scale of spatial features while simultaneously reducing computational requirements for large satellite images, we propose an architecture of two cascaded CNN model components successively processing undersampled and full resolution images. The first component distinguishes between patches in the inner cloud area from patches at the cloud's boundary region. For the cloud-ambiguous edge patches requiring further segmentation, the framework then delegates computation to a fine-grained model component. We apply the architecture to a cloud detection dataset of complete Sentinel-2 multispectral images, approximately annotated for minimal false negatives in a land use application. On this specific task and data, we achieve a 16\% relative improvement in pixel accuracy over a CNN baseline based on patching.