Two methods for reconstructing intragranular strain fields are developed for scanning three-dimensional X-ray diffraction (3DXRD). The methods are compared with a third approach where voxels are reconstructed independently of their neighbours [Hayashi, Setoyama & Seno (2017). Mater. Sci. Forum, 905, 157–164]. The 3D strain field of a tin grain, located within a sample of approximately 70 grains, is analysed and compared across reconstruction methods. Implicit assumptions of sub-problem independence, made in the independent voxel reconstruction method, are demonstrated to introduce bias and reduce reconstruction accuracy. It is verified that the two proposed methods remedy these problems by taking the spatial properties of the inverse problem into account. Improvements in reconstruction quality achieved by the two proposed methods are further supported by reconstructions using synthetic diffraction data.