This paper describes a shape-from-shading algorithm that combines constraint on data-closeness from Lambert's law and Fourier domain integrability. The data closeness is ensured by constraining surface normals to fall on an irradiance cone, whose axis points in the light source direction and whose apex angle varies with iteration number. The integrability is ensured by projecting the non-integrable set of surface normals to the nearest integrable one by globally minimizing the distance among them in the Fourier domain. The combination of both data-closeness and integrability constraints is aimed to overcome the problem of high dependency on the image irradiances. Experimental results prove that the new method recovers needle maps that are both smooth and integrable and improves height surface stability.