Advances in deep learning techniques have allowed recent work to reconstruct the shape of a single object given only one RBG image as input. Building on common encoder-decoder architectures for this task, we propose three extensions: (1) ray-traced skip connections that propagate local 2D information to the output 3D volume in a physically correct manner; (2) a hybrid 3D volume representation that enables building translation equivariant models, while at the same time encoding fine object details without an excessive memory footprint; (3) a reconstruction loss tailored to capture overall object geometry. Furthermore, we adapt our model to address the harder task of reconstructing multiple objects from a single image. We reconstruct all objects jointly in one pass, producing a coherent reconstruction, where all objects live in a single consistent 3D coordinate frame relative to the camera and they do not intersect in 3D space. We also handle occlusions and resolve them by hallucinating the missing object parts in the 3D volume. We validate the impact of our contributions experimentally both on synthetic data from ShapeNet as well as real images from Pix3D. Our method outperforms the state-of-the-art single-object methods on both datasets. Finally, we evaluate performance quantitatively on multiple object reconstruction with synthetic scenes assembled from ShapeNet objects.