The ability to see around corners, i.e., recover details of a hidden scene from its reflections in the surrounding environment, is of considerable interest in a wide range of applications. However, the diffuse nature of light reflected from typical surfaces leads to mixing of spatial information in the collected light, precluding useful scene reconstruction. Here, we employ a computational imaging technique that opportunistically exploits the presence of occluding objects, which obstruct probe-light propagation in the hidden scene, to undo the mixing and greatly improve scene recovery. Importantly, our technique obviates the need for the ultrafast time-of-flight measurements employed by most previous approaches to hidden-scene imaging. Moreover, it does so in a photon-efficient manner based on an accurate forward model and a computational algorithm that, together, respect the physics of three-bounce light propagation and single-photon detection. Using our methodology, we demonstrate reconstruction of hiddensurface reflectivity patterns in a meter-scale environment from non-time-resolved measurements. Ultimately, our technique represents an instance of a rich and promising new imaging modality with important potential implications for imaging science.