  In this paper we consider the hyperbolic-elliptic Ishimori initial-value
problem. We prove that such system is locally well-posed for small data in
$H^{s}$ level space, for $s> 3/2$. The new ingredient is that we develop the
methods of Ionescu and Kenig \cite{IK} and \cite{IK2} to approach the problem
in a perturbative way.
