Near the tip of the stau coannihilation strip in the CMSSM with a neutralino LSP, the astrophysical cold dark matter density constraint forces the stau-neutralino mass difference to be small. If this mass difference is less than the mass of the tau lepton, the stau may decay either in the outer part of an LHC detector -- giving a "disappearing track" signature -- or be sufficiently long-lived to leave the detector before decaying, thus giving the long-lived massive charged-particle signature. We combine limits from searches for these signatures with those from conventional missing ET searches during LHC Run 1, identifying the small remaining parts of the CMSSM stau-coannihilation strip region that have not yet been excluded, and discussing how they may be explored during Run 2 of the LHC.