The classes of Type IIb, Ib, and Ic core-collapse supernovae appear to represent progressively greater stripping of the progenitor star's outer envelope prior to explosion, but it is unclear how much of this stripping is due to stellar winds and mass-loss, or to interaction with a massive binary companion. We have used the Hubble Space Telescope to search for surviving binary companions to nearby stripped-envelope supernovae in the ultraviolet. I will describe our results for the broad-lined Type Ic SN 2002ap, and for the Type IIb SN 2001ig.