  This article shows that knowledge of the Dirichlet-Neumann map on certain
subsets of the boundary for input functions supported roughly on the rest of
the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With
some geometric conditions on the domain, either the subset on which the DN map
is measured or the subset on which the input functions have support may be made
arbitrarily small. This is an improvement on the partial data result in a paper
by Dos Santos Ferreira, Kenig, Sj\"{o}strand, and Uhlmann. The method involves
modifying the Carleman estimate in that paper by conjugation with operators
built from pseudodifferential pieces.
