  We show the validity of Nachman's procedure (Ann. Math., 128(3):531--576,
1988) for reconstructing a conductivity $\gamma$ from its Dirichlet-to-Neumann
map $\Lambda_\gamma$ for less regular conductivities, specifically $\gamma \in
W^{3/2,2n}(\Omega)$ such that $\gamma \equiv 1$ near $\partial \Omega$. We also
obtain a log-type stability estimate for the inverse problem when in addition,
$\gamma \in W^{2-s,n/s}(\Omega)$ for $0 < s <1/2$.
