IceCube’s measurements of the astrophysical neutrino flux have applied veto techniques to suppress atmospheric neutrinos and muons. All the vetos thus far have used the outer regions of the detector to identify and reject penetrating muon tracks, leaving the inner parts of the detector available to observe the astrophysical neutrino flux. Here we discuss a method that is optimized for muon neutrinos which have a charged-current interaction with a contained vertex. This analysis exploits the high quality directional information of muons to determine a veto on an event by event basis. The final sample will contain astrophysical neutrinos with good purity starting around 10 TeV.