(joint work with M. Möller) The complexity of singular fibers of the Hitchin system stems from the variety of singularities of the spectral curve. In this talk I will explain how to modify the rank 2 Hitchin base, such that the family of spectral curves can be resolved to a family of semi-stable nodal curves. This allows to extend the Hitchin system to the singular locus of the modified Hitchin base by well-understood compactified Jacobians of semi-stable curves