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