We present a new technique for estimating the 3D shape of an object that combines previous ideas from shape from silhouettes and shape from shadows. We begin with a set-up for robustly extracting object silhouettes by casting a shadow of the object with a point light-source onto a translucent panel. A camera on the opposite side of the panel records an image which is readily processed to obtain the object boundary. We use a space carving technique to extract an initial estimate of the object shape. In a second phase, we record a series of images of the object lit by point light sources. We compare the areas of self shadowing in these images to those expected if our estimated shape from the space carving were correct. The shape of the object is refined by a shadow carving step that adjusts the current shape to resolve contradictions between the captured images and the current shape estimate. The result of the space carving and shadow carving is an estimate of shape that can be further refined by methods that work well in local regions, such as photometric stereo. We have implemented our approach in a simple table top system and present the results of scanning a small object with deep concavities.