Existing GAN inversion and editing methods work well for aligned objects with a clean background, such as portraits and animal faces, but often struggle for more difficult categories with complex scene layouts and object occlusions, such as cars, animals, and outdoor images. We propose a new method to invert and edit such complex images in the latent space of GANs, such as StyleGAN2. Our key idea is to explore inversion into a collection of layers, spatially adapting the inversion process to the difficulty of the image. We learn to predict the ``invertibility'' of different segments of the image and project each segment into a latent layer. Easier regions can be inverted into an earlier layer in the generator's latent space, while more challenging regions can be inverted into a later feature space. Experiments show that our method obtains better inversion results compared to the state-of-the-art approaches on complex categories like cars, cats, and horses, while maintaining the downstream editability.