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The DAMA collaboration reported an annually modulated rate compatible with a Dark Matter induced signal. I will show how a slowly varying rate can bias or even simulate an annual modulation, if data are analyzed in terms of residuals computed by subtracting approximately yearly averages, rather than a background continuous in time. In the most extreme case, the amplitude and phase of the annual modulation reported by DAMA could be alternatively interpreted as a decennial growth of the rate. This possibility appears mildly disfavoured by a detailed study of the available data, but cannot be safely excluded. In general, a decreasing or increasing rate could partially reduce or enhance a true annual modulation, respectively. The issue could be clarified by looking at the full time-dependence of the DAMA total rate, not explicitly published so far.