  We construct a theory of coherent transport through a ballistic quantum dot
coupled to a superconductor. We show that the leading-order quantum correction
to the two-terminal conductance of these Andreev quantum dots may change sign
depending on (i) the number of channels carried by the normal leads or (ii) the
magnetic flux threading the dot. In contrast, spin-orbit interaction may affect
the magnitude of the correction, but not always its sign. Experimental
signatures of the effect include a non-monotonic magnetoconductance curve and a
transition from an insulator-like to a metal-like temperature dependence of the
conductance. Our results are applicable to ballistic or disordered dots.
