I will present some results concerning the higher gradient integrability of σ-harmonic functions u with discontinuous coefficients σ, i.e., weak solutions of div(σ∇u) = 0. When σ is assumed to be symmetric, then the optimal integrability exponent of the gradient field is known thanks to the work of Astala and Leonetti & Nesi. I will discuss the case when only the ellipticity is fixed and σ is otherwise unconstrained and show that the optimal exponent is attained on the class of two-phase conductivities σ : Ω ⊂ R^2 → {σ_1,σ_2} ⊂ M^2×2. For such a class we also characterise the minimal exponent q ∈ (1, 2) and the maximal exponent p > 2 such that if ∇u ∈ L^q then ∇u ∈ L^p_weak. (Joint work with Nesi & Ponsiglione and S. Fanzon.)