Hi Mike,
In the image below the left most object is the original poly cube object. The middle one is the same object in a hypernurbs cage. The one on the right is the same onbect in a hypernurbs cage after using the knife tool close to the existing vertices. You'll probably want to drag the poly object outside of the cage for a moment so you can accurately make the cuts, but the depends on the particular situation.
By selecting points created by the knife tool and dragging them closer/farther from the original vertices (original edge prior to using the knife), you can control just how sharp you want the edge to be.
Mark Simpson
