The dark matter abundance may follow from a primordial asymmetry, if dark matter is charged under a conserved quantum number. It is often stated that such "Asymmetric Dark Matter" models predict a dark matter mass around the GeV scale. We propose a new realization of asymmetric dark matter, where the dark matter and lepton asymmetries are generated simultaneously through two-sector leptogenesis. We will see that the dark matter mass can range from 1 keV to 10 TeV, while producing the correct abundance. This opens up a much wider parameter space for asymmetric dark matter. We will highlight varieties of this framework that have interesting consequences for the indirect detection of dark matter.