  We extend a global uniqueness result for the Calder\'on problem with partial
data, due to Kenig-Sj\"ostrand-Uhlmann, to the case of less regular
conductivities. Specifically, we show that in dimensions $n\ge 3$, the
knowledge of the Diricihlet-to-Neumann map, measured on possibly very small
subsets of the boundary, determines uniquely a conductivity having essentially
$3/2$ derivatives in an $L^2$ sense.
