Compositing virtual objects into real background images requires one to carefully match the scene’s camera parameters, surface geometry, textures, and lighting to obtain plausible renderings. Recent learning approaches have shown many scene properties can be estimated from images, resulting in robust automatic single-image compositing systems, but many challenges remain. In particular, interactions between real and synthetic shadows are not handled gracefully by existing methods, which typically assume a shadow-free background. As a result, they tend to generate double shadows when the synthetic object’s cast shadow overlaps a background shadow, and ignore shadows from the background that should be cast onto the synthetic object. In this paper, we present a compositing method for outdoor scenes that addresses these issues and produces realistic cast shadows. This requires identifying existing shadows, including soft shadow boundaries, then reasoning about the ambiguity of unknown ground albedo and scene lighting to match the color and intensity of shaded areas. Using supervision from shadow removal and detection datasets, we propose a generative adversarial pipeline and improved composition equations that simultaneously handle both shadow interaction scenarios. We evaluate our method on challenging, real outdoor images from multiple distributions and datasets. Quantitative and qualitative comparisons show our approach produces more realistic results than existing alternatives. Our code, datasets, and trained models are publicly available at https://lvsn.github.io/shadowcompositing.