Abstract: We show how constraints on the time integrated event rate from a given dark matter (DM) direct detection experiment can be used to bound the amplitude of the annual modulation signal in another experiment. The method requires only mild assumptions about the properties of the local DM distribution: that it is temporally stable on the scale of months and spatially homogeneous on the ecliptic. We apply the method to the annual modulation signal in DAMA/LIBRA, which we compare to the bounds derived from XENON10, XENON100, cryogenic DM search, and SIMPLE data. Assuming a DM mass of 10 GeV, we show that under the above assumptions about the DM halo, a DM interpretation of the DAMA/LIBRA signal is excluded for several classes of models: at 6.3 sigma (4.6 sigma) for elastic isospin conserving (violating) spin-independent interactions, and at 4.9 sigma for elastic spin-dependent interactions on protons.