  We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono
equation \[\partial_t u+|\partial_x|^{1+\alpha}\partial_x u+uu_x=0,\
u(x,0)=u_0(x),\] is locally well-posed in the Sobolev spaces $H^s$ for
$s>1-\alpha$ if $0\leq \alpha \leq 1$. The new ingredient is that we develop
the methods of Ionescu, Kenig and Tataru \cite{IKT} to approach the problem in
a less perturbative way, in spite of the ill-posedness results of Molinet, Saut
and Tzvetkovin \cite{MST}. Moreover, as a bi-product we prove that if $0<\alpha
\leq 1$ the corresponding modified equation (with the nonlinearity $\pm uuu_x$)
is locally well-posed in $H^s$ for $s\geq 1/2-\alpha/4$.
