We compare the sensitivity of WIMP detection via direct separation of possible signal vs. background to WIMP detection via detection of an annual modulation, in which signal and background cannot be separated on an event-by-event basis. In order to determine how the constraints from the two different types of experiments might be combined an adequate incorporation of uncertainties due to galactic halo models must be made. This issue is particularly timely in light of recent direct detection limits from Edelweiss and CDMS, which we now demonstrate cannot be made consistent with a recent claimed DAMA annual modulation observation, even by including halo uncertainties. On the other hand, we demonstrate that a combination of these two techniques, in the event of any positive direct detection signal, could ultimately allow significant constraints on anisotropic halo models even without directional sensitivity in these detectors.