Several galaxies have exhibited X-ray flares that are consistent with the tidal disruption of a star by a central supermassive black hole. In theoretical treatments of this process it is usually assumed that the star was initially on a nearly parabolic orbit relative to the black hole. Such an assumption leads in the simplest approximation to a t−5/3 decay of the bolometric luminosity and this is indeed consistent with the relatively poorly sampled light curves of such flares. We point out that there is another regime in which the decay would be different: if a binary is tidally separated and the star that remains close to the hole is eventually tidally disrupted from a moderate eccentricity orbit, the decay is slower, typically ∼t−1.2. As a result, careful sampling of the light curves of such flares could distinguish between these processes and yield insight into the dynamics of binaries as well as single stars in galactic centres. We explore this process using three-body simulations and analytic treatments and discuss the consequences for present-day X-ray detections and future gravitational wave observations.