We consider the Cauchy problem of derivative nonlinear Schrödinger type equations. We prove the local well-posedness around bounded functions, such as kink solutions. Our argument is based on the energy method using the dispersive nature of the equation. In order to go below H^1, we use a cancellation property that was previously observed in the study of KdV type equations with low dispersion. This talk is based on a joint work with Luc Molinet (Univ. of Tours).