We show that the approaches to 3D reconstruction that use volumetric graph cuts to minimize a cost function over the object surface have two types of biases, the minimal surface bias and the discretization bias. These biases make it difficult to recover surface extrusions and other details, especially when a non-lambertian photo-consistency measure is used. To reduce these biases, we propose a new iterative graph cuts based algorithm that operates on the Surface Distance Grid (SDG), which is a special discretization of the 3D space, constructed using a signed distance transform of the current surface estimate. It can be shown that SDG significantly reduces the minimal surface bias, and transforms the discretization bias into a controllable degree of surface smoothness. Experiments on 3D reconstruction of non-lambertian objects confirm the effectiveness of our algorithm over previous methods.