  Highly pixelated solid-state detectors offer outstanding capabilities in the
identification and suppression of backgrounds from natural radioactivity. We
present the background-identification strategies developed for the DAMIC
experiment, which employs silicon charge-coupled devices to search for dark
matter. DAMIC has demonstrated the capability to disentangle and measure the
activities of every $\beta$ emitter from the $^{32}$Si, $^{238}$U and
$^{232}$Th decay chains in the silicon target. Similar strategies will be
adopted by the Selena Neutrino Experiment, which will employ hybrid amorphous
$^{82}$Se/CMOS imagers to perform spectroscopy of $\beta\beta$ decay and solar
neutrinos. We present the proposed experimental strategy for Selena to achieve
zero-background in a 100-ton-year exposure.
