We present a novel high-fidelity generative adversarial network (GAN) inversion framework that enables attribute editing with image-specific details well-preserved (e.g., background, appearance and illumination). We first formulate GAN inversion as a lossy data compression problem and carefully discuss the Rate-Distortion-Edit trade-off. Due to this trade-off, previous works fail to achieve high-fidelity reconstruction while keeping compelling editing ability with a low bit-rate latent code only. In this work, we propose a distortion consultation approach that employs the distortion map as a reference for reconstruction. In the distortion consultation inversion (DCI), the distortion map is first projected to a high-rate latent map, which then complements the basic low-rate latent code with (lost) details via consultation fusion. To achieve high-fidelity editing, we propose an adaptive distortion alignment (ADA) module with a self-supervised training scheme. Extensive experiments in the face and car domains show a clear improvement in terms of both inversion and editing quality.