In recent years we have witnessed tremendous progress in unpaired image-to-image translation, propelled by the emergence of DNNs and adversarial training strategies. However, most existing methods focus on transfer of style and appearance, rather than on shape translation. The latter task is challenging, due to its intricate non-local nature, which calls for additional supervision. We mitigate this by descending the deep layers of a pre-trained network, where the deep features contain more semantics, and applying the translation between these deep features. Our translation is performed in a cascaded, deep-to-shallow, fashion, along the deep feature hierarchy: we first translate between the deepest layers that encode the higher-level semantic content of the image, proceeding to translate the shallower layers, conditioned on the deeper ones. We further demonstrate the effectiveness of using pre-trained deep features in the context of unconditioned image generation. Our code and trained models will be made publicly available.