  We consider hyperbolic 3-manifolds with either non-empty compact geodesic
boundary, or some toric cusps, or both. For any such M we analyze what portion
of the volume of M can be recovered by inserting in M boundary collars and cusp
neighbourhoods with disjoint embedded interiors. Our main result is that this
portion can only be maximal in some combinatorially extremal configurations.
The techniques we employ are VERY elementary but the result is in our opinion
of some interest.
