Some new results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation [katex]\bar\partial f = \mu \partial f + \nu\, \overline{\partial f}[/katex] for discontinuous Beltrami coefficients [katex]\mu[/katex] and [katex]\nu[/katex] are obtained, using Kato-Ponce commutators. A conjecture on the cases where the limitations of the method do not work is raised.