We analyse the electrical conductance G(phi) of a two-dimensional, phase-coherent structure in contact with two superconductors, which is known to be an oscillatory function of the phase difference phi between the superconductors. It is predicted that for a ballistic sample, the amplitude of oscillation will be enhanced by placing a normal barrier at the normal-superconducting interface, and that by tuning the strength of the barrier, it can be made orders of magnitude greater than values observed in recent experiments. Giant oscillations can also be obtained without a barrier, provided that a crucial sum rule is broken. This can be achieved by disorder-induced normal scattering. In the absence of zero-phase inter-channel scattering, the conductance possesses a zero-phase minimum and a maximum at phi = pi.