Simplified models are a successful way of interpreting current LHC searches for models beyond the standard model (BSM). So far most simplified models have focused on topologies featuring a missing transverse energy (MET) signature. However, in some BSM theories other, more exotic, signatures occur. We discuss the utility of applying the simplified models framework to exotic signatures, such as heavy stable charged particles (HSCP). As a physical application we investigate the CMSSM stau co-annihilation strip containing long-lived staus, which presents a potential solution to the Lithium problem. Applying both MET and HSCP constraints we show that, for low values of tanβ, all this region of parameter space either violates Dark Matter constraints or is excluded by LHC searches.